references.bib

@article{sparsebathfitting2021, 
year = {2021}, 
title = {{Sparse modeling of large-scale quantum impurity models with low symmetries}}, 
author = {Shinaoka, Hiroshi and Nagai, Yuki}, 
journal = {Physical Review B}, 
issn = {2469-9950}, 
doi = {10.1103/physrevb.103.045120}, 
abstract = {{Quantum embedding theories can be used for obtaining quantitative descriptions of correlated materials. However, a critical challenge is solving an effective impurity model of correlated orbitals embedded in an electron bath. Many advanced impurity solvers require the approximation of a bath continuum using a finite number of bath levels, producing a highly nonconvex, ill-conditioned inverse problem. To address this drawback, this study proposes an efficient fitting algorithm for matrix-valued hybridization functions based on a data-science approach, sparse modeling, and a compact representation of Matsubara Green's functions. The efficiency of the proposed method is demonstrated by fitting random hybridization functions with large off-diagonal elements and those of a 20-orbital impurity model for a high-Tc compound, LaAsFeO, at low temperatures (T). The results set quantitative goals for the future development of impurity solvers toward quantum embedding simulations of complex correlated materials.}}, 
pages = {045120}, 
number = {4}, 
volume = {103}, 
local-url = {file://localhost/Users/hiroshi/Desktop/Add%20to%20Papers/PhysRevB.103.045120.pdf}
}
@article{Li:2020eu, 
year = {2020}, 
rating = {0}, 
title = {{Sparse sampling approach to efficient ab initio calculations at finite temperature}}, 
author = {Li, Jia and Wallerberger, Markus and Chikano, Naoya and Yeh, Chia-Nan and Gull, Emanuel and Shinaoka, Hiroshi}, 
journal = {Physical Review B}, 
doi = {10.1103/physrevb.101.035144}, 
abstract = {{Phys. Rev. B 101, 035144 (2020). doi:10.1103/PhysRevB.101.035144}}, 
pages = {035144}, 
number = {3}, 
volume = {101}, 
language = {English}, 
keywords = {}, 
month = {01}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Li-2020-Physical%20Review%20B.pdf}
}
@article{Shinaoka:2020ji, 
year = {2020}, 
rating = {0}, 
title = {{Sparse sampling and tensor network representation of two-particle Green's functions}}, 
author = {Shinaoka, Hiroshi and Geffroy, Dominique and Wallerberger, Markus and Otsuki, Junya and Yoshimi, Kazuyoshi and Gull, Emanuel and Kuneš, Jan}, 
journal = {SciPost Physics}, 
issn = {2542-4653}, 
doi = {10.21468/scipostphys.8.1.012}, 
url = {https://scipost.org/SciPostPhys.8.1.012/pdf}, 
pages = {012 -- 23}, 
number = {1}, 
volume = {8}, 
keywords = {}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Shinaoka-2020-SciPost%20Physics.pdf}
}
@article{Otsuki:2020fn, 
year = {2020}, 
rating = {0}, 
title = {{Sparse Modeling in Quantum Many-Body Problems}}, 
author = {Otsuki, Junya and Ohzeki, Masayuki and Shinaoka, Hiroshi and Yoshimi, Kazuyoshi}, 
journal = {Journal of the Physical Society of Japan}, 
doi = {10.7566/jpsj.89.012001}, 
pages = {012001}, 
number = {1}, 
volume = {89}, 
language = {English}, 
month = {01}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Otsuki-2020-Journal%20of%20the%20Physical%20Society%20of%20Japan.pdf}
}
@article{Kaltak2020, 
year = {2020}, 
title = {{Minimax isometry method: A compressive sensing approach for Matsubara summation in many-body perturbation theory}}, 
author = {Kaltak, Merzuk and Kresse, Georg}, 
journal = {Physical Review B}, 
issn = {2469-9950}, 
doi = {10.1103/physrevb.101.205145}, 
eprint = {1909.01740}, 
abstract = {{We present a compressive sensing approach for the long-standing problem of Matsubara summation in many-body perturbation theory. By constructing low-dimensional, almost isometric subspaces of the Hilbert space we obtain optimum imaginary time and frequency grids that allow for extreme data compression of fermionic and bosonic functions in a broad temperature regime. The method is applied to the random phase and self-consistent GW approximation of the grand potential. Integration and transformation errors are investigated for Si and SrVO3.}}, 
pages = {205145}, 
number = {20}, 
volume = {101}
}
@article{NomuraRR2020, 
year = {2020}, 
title = {{Magnetic exchange coupling in cuprate-analog d9 nickelates}}, 
author = {Nomura, Yusuke and Nomoto, Takuya and Hirayama, Motoaki and Arita, Ryotaro}, 
journal = {Physical Review Research}, 
doi = {10.1103/physrevresearch.2.043144}, 
eprint = {2006.16943}, 
abstract = {{Motivated by the recent discovery of superconductivity in doped NdNiO2, we study the magnetic exchange interaction J in layered d9 nickelates from first principles. The mother compounds of the high-Tc cuprates belong to the charge-transfer regime in the Zaanen-Sawatzky-Allen diagram and have J larger than 100 meV. While this feature makes the cuprates very different from other transition metal oxides, it is of great interest whether layered d9 nickelates can also have such a large J. However, one complexity is that NdNiO2 is not a Mott insulator due to carrier doping from the block layer. To compare the cuprates and d9 nickelates on an equal basis, we study RbCa2NiO3 and A2NiO2Br2 (A denotes a cation with a valence of 2.5+), which were recently designed theoretically by block-layer engineering. These nickelates are free from the self-doping effect and belong to the Mott-Hubbard regime. We show that these nickelates share a common thread with the high-Tc cuprates in that they also have a significant exchange interaction J as large as about 100 meV.}}, 
pages = {043144}, 
number = {4}, 
volume = {2}, 
local-url = {file://localhost/Users/hiroshi/Desktop/Add%20to%20Papers/PhysRevResearch.2.043144.pdf}
}
@article{NomotoPRB2020, 
year = {2020}, 
title = {{Local force method for the ab initio tight-binding model: Effect of spin-dependent hopping on exchange interactions}}, 
author = {Nomoto, Takuya and Koretsune, Takashi and Arita, Ryotaro}, 
journal = {Physical Review B}, 
issn = {2469-9950}, 
doi = {10.1103/physrevb.102.014444}, 
eprint = {2003.11162}, 
abstract = {{To estimate the Curie temperature of metallic magnets from first principles, we develop a local force method for the tight-binding model having spin-dependent hopping derived from spin-density-functional theory. While spin-dependent hopping is crucial for the self-consistent mapping to the effective spin model, the numerical cost to treat such nonlocal terms in the conventional Green's function scheme is formidably expensive. Here, we propose a formalism based on the kernel polynomial method (KPM), which makes the calculation dramatically efficient. We perform a benchmark calculation for bcc-Fe, fcc-Co, and fcc-Ni and find that the effect of the magnetic nonlocal terms is particularly prominent for bcc-Fe. We also present several local approximations to the magnetic nonlocal terms for which we can apply the Green's function method and reduce the numerical cost further by exploiting the intermediate representation of the Green's function. By comparing the results of the KPM and local methods, we discuss which local method works most successfully. Our approach provides an efficient way to estimate the Curie temperature of metallic magnets with a complex spin configuration.}}, 
pages = {014444}, 
number = {1}, 
volume = {102}, 
local-url = {file://localhost/Users/hiroshi/Desktop/Add%20to%20Papers/PhysRevB.102.014444.pdf}
}
@article{NomotoPRL2020, 
year = {2020}, 
title = {{Formation Mechanism of the Helical Q Structure in Gd-Based Skyrmion Materials}}, 
author = {Nomoto, Takuya and Koretsune, Takashi and Arita, Ryotaro}, 
journal = {Physical Review Letters}, 
issn = {0031-9007}, 
doi = {10.1103/physrevlett.125.117204}, 
pmid = {32975986}, 
eprint = {2003.13167}, 
abstract = {{Using the ab initio local force method, we investigate the formation mechanism of the helical spin structure in GdRu2Si2 and Gd2PdSi3. We calculate the paramagnetic spin susceptibility and find that the Fermi surface nesting is not the origin of the incommensurate modulation, in contrast to the naive scenario based on the Ruderman-Kittel-Kasuya-Yosida mechanism. We then decompose the exchange interactions between the Gd spins into each orbital component, and show that spin-density-wave type interaction between the Gd-5d orbitals is ferromagnetic, but the interaction between the Gd-4f orbitals is antiferromagnetic. We conclude that the competition of these two interactions, namely, the interorbital frustration, stabilizes the finite-Q structure.}}, 
pages = {117204}, 
number = {11}, 
volume = {125}, 
local-url = {file://localhost/Users/hiroshi/Desktop/Add%20to%20Papers/PhysRevLett.125.117204.pdf}
}
@article{Wang2020, 
year = {2020}, 
title = {{Efficient ab initio Migdal-Eliashberg calculation considering the retardation effect in phonon-mediated superconductors}}, 
author = {Wang, Tianchun and Nomoto, Takuya and Nomura, Yusuke and Shinaoka, Hiroshi and Otsuki, Junya and Koretsune, Takashi and Arita, Ryotaro}, 
journal = {Physical Review B}, 
issn = {2469-9950}, 
doi = {10.1103/physrevb.102.134503}, 
abstract = {{We formulate an efficient scheme to perform a Migdal-Eliashberg calculation considering the retardation effect from first principles. While the conventional approach requires a huge number of Matsubara frequencies, we show that the intermediate representation of the Green's function [H. Shinaoka , Phys. Rev. B 96, 035147 (2017)10.1103/PhysRevB.96.035147] dramatically reduces the numerical cost to solve the linearized gap equation. Without introducing any empirical parameter, we obtain a superconducting transition temperature of elemental Nb (∼10 K), which is consistent with experiment. The present result indicates that our approach has a superior performance for many superconductors for which Tc is lower than O(10) K.}}, 
pages = {134503}, 
number = {13}, 
volume = {102}, 
local-url = {file://localhost/Users/hiroshi/Desktop/Add%20to%20Papers/PhysRevB.102.134503.pdf}
}
@article{Witt_IR_FLEX,
  title = {Efficient fluctuation-exchange approach to low-temperature spin fluctuations and superconductivity: From the Hubbard model to ${\mathrm{Na}}_{x}{\mathrm{CoO}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}{y\mathrm{H}}_{2}\mathrm{O}$},
  author = {Witt, Niklas and van Loon, Erik G. C. P. and Nomoto, Takuya and Arita, Ryotaro and Wehling, Tim O.},
  journal = {Phys. Rev. B},
  volume = {103},
  issue = {20},
  pages = {205148},
  numpages = {12},
  year = {2021},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.103.205148},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.103.205148}
}

@article{Witt_IR_FLEX_, 
year = {2020}, 
title = {{An efficient fluctuation exchange approach to low-temperature spin fluctuations and superconductivity: from the Hubbard model to Na\$\_x\$CoO\$\_2\textbackslashcdot y\$H\$\_2\$O}}, 
author = {Witt, Niklas and Loon, Erik G C P van and Nomoto, Takuya and Arita, Ryotaro and Wehling, Tim}, 
journal = {arXiv}, 
eprint = {2012.04562}, 
abstract = {{Superconductivity arises mostly at energy and temperature scales that are much smaller than the typical bare electronic energies. Since the computational effort of diagrammatic many-body techniques increases with the number of required Matsubara frequencies and thus with the inverse temperature, phase transitions that occur at low temperatures are typically hard to address numerically. In this work, we implement a fluctuation exchange (FLEX) approach to spin fluctuations and superconductivity using the "intermediate representation basis" (IR) [Shinaoka et al., PRB 96, 2017] for Matsubara Green functions. This FLEX+IR approach is numerically very efficient and enables us to reach temperatures on the order of \$10\textasciicircum\{-4\}\$ in units of the electronic band width in multi-orbital systems. After benchmarking the method in the doped repulsive Hubbard model on the square lattice, we study the possibility of spin-fluctuation-mediated superconductivity in the hydrated sodium cobalt material Na\$\_x\$CoO\$\_2\textbackslashcdot y\$H\$\_2\$O reaching the scale of the experimental transition temperature \$T\_\{\textbackslashmathrm\{c\}\}=4.5\$ K and below.}}
}
@article{Isakov2020, 
year = {2020}, 
title = {{Ab initio self-energy embedding for the photoemission spectra of NiO and MnO}}, 
author = {Iskakov, Sergei and Yeh, Chia-Nan and Gull, Emanuel and Zgid, Dominika}, 
journal = {Physical Review B}, 
issn = {2469-9950}, 
doi = {10.1103/physrevb.102.085105}, 
eprint = {2003.04440}, 
abstract = {{The accurate ab initio simulation of periodic solids with strong correlations is one of the grand challenges of condensed matter. While mature methods exist for weakly correlated solids, the ab initio description of strongly correlated systems is an active field of research. In this work, we show results for the single-particle spectral function of the two correlated d-electron solids NiO and MnO from self-energy embedding theory. Unlike earlier work, the theory does not use any adjustable parameters and is fully ab initio, while being able to treat both the strong correlation and the nonlocal screening physics of these materials. We derive the method, discuss aspects of the embedding and choices of physically important orbitals, and compare our results to x-ray and angle-resolved photoemission spectroscopy as well as bremsstrahlung-isochromat spectroscopy.}}, 
pages = {085105}, 
number = {8}, 
volume = {102}, 
local-url = {file://localhost/Users/hiroshi/Desktop/Add%20to%20Papers/PhysRevB.102.085105.pdf}
}
@article{Otsuki:2019bz, 
year = {2019}, 
rating = {0}, 
title = {{Strong-coupling formula for momentum-dependent susceptibilities in dynamical mean-field theory}}, 
author = {Otsuki, Junya and Yoshimi, Kazuyoshi and Shinaoka, Hiroshi and Nomura, Yusuke}, 
journal = {Physical Review B}, 
doi = {10.1103/physrevb.99.165134}, 
abstract = {{Phys. Rev. B 99, 165134 (2019). doi:10.1103/PhysRevB.99.165134}}, 
pages = {165134}, 
number = {16}, 
volume = {99}, 
language = {English}, 
month = {04}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Otsuki-2019-Physical%20Review%20B.pdf}
}
@article{Takeshita.2019.Rabani, 
year = {2019}, 
title = {{Stochastic resolution of identity second-order Matsubara Green’s function theory}}, 
author = {Takeshita, Tyler Y and Dou, Wenjie and Smith, Daniel G A and Jong, Wibe A de and Baer, Roi and Neuhauser, Daniel and Rabani, Eran}, 
journal = {The Journal of Chemical Physics}, 
issn = {0021-9606}, 
doi = {10.1063/1.5108840}, 
pmid = {31370516}, 
abstract = {{We develop a stochastic resolution of identity representation to the second-order Matsubara Green's function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/contractions, which reduces the computational cost from O(N5) to O(N3) (with N being the number of atomic orbitals). The current approach can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 103 electrons and more.}}, 
pages = {044114}, 
number = {4}, 
volume = {151}
}
@article{Yoshimi:2019bt, 
year = {2019}, 
rating = {0}, 
title = {{SpM: Sparse modeling tool for analytic continuation of imaginary-time Green's function}}, 
author = {Yoshimi, Kazuyoshi and Otsuki, Junya and Motoyama, Yuichi and Ohzeki, Masayuki and Shinaoka, Hiroshi}, 
journal = {Computer Physics Communications}, 
doi = {10.1016/j.cpc.2019.07.001}, 
abstract = {{Computer Physics Communications, 244 (2019) 319-323. doi:10.1016/j.cpc.2019.07.001}}, 
pages = {319 -- 323}, 
volume = {244}, 
language = {English}, 
month = {11}
}
@article{Nagai:2019dea, 
year = {2019}, 
rating = {0}, 
title = {{Smooth Self-energy in the Exact-diagonalization-based Dynamical Mean-field Theory: Intermediate-representation Filtering Approach}}, 
author = {Nagai, Yuki and Shinaoka, Hiroshi}, 
journal = {Journal of the Physical Society of Japan}, 
doi = {10.7566/jpsj.88.064004}, 
pages = {064004 -- 5}, 
number = {6}, 
volume = {88}, 
language = {English}, 
month = {06}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Nagai-Smooth%20Self-energy%20in%20the%20Exact-diagonalization-based%20Dynamical%20Mean-field%20Theory-%20Intermediate-representation%20Filtering%20Approach-2019-Journal%20of%20the%20Physical%20Society%20of%20Japan.pdf}
}
@article{Schüler.2018.Pavlyukh, 
year = {2018}, 
title = {{Spectral properties from Matsubara Green's function approach: Application to molecules}}, 
author = {Schüler, M. and Pavlyukh, Y.}, 
journal = {Physical Review B}, 
issn = {2469-9950}, 
doi = {10.1103/physrevb.97.115164}, 
eprint = {1710.08660}, 
abstract = {{We present results for many-body perturbation theory for the one-body Green's function at finite temperatures using the Matsubara formalism. Our method relies on the accurate representation of the single-particle states in standard Gaussian basis sets, allowing to efficiently compute, among other observables, quasiparticle energies and Dyson orbitals of atoms and molecules. In particular, we challenge the second-order treatment of the Coulomb interaction by benchmarking its accuracy for a well-established test set of small molecules, which includes also systems where the usual Hartree-Fock treatment encounters difficulties. We discuss different schemes how to extract quasiparticle properties and assess their range of applicability. With an accurate solution and compact representation, our method is an ideal starting point to study electron dynamics in time-resolved experiments by the propagation of the Kadanoff-Baym equations.}}, 
pages = {115164}, 
number = {11}, 
volume = {97}
}
@article{Chikano:2018gd, 
year = {2018}, 
rating = {0}, 
title = {{Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function}}, 
author = {Chikano, Naoya and Otsuki, Junya and Shinaoka, Hiroshi}, 
journal = {Physical Review B}, 
doi = {10.1103/physrevb.98.035104}, 
abstract = {{The imaginary-time Green's function is a building block of various numerical methods for correlated electron systems. Recently, it was shown that a model-independent compact orthogonal representation of the Green's function can be constructed by decomposing its spectral representation. We investigate the performance of this so-called intermediate representation (IR) from several points of view. First, we develop an efficient algorithm for computing the IR basis functions of arbitrary high degree. Second, for two simple models, we study the number of coefficients required to represent the Green's function within a given tolerance. We show that the number of coefficients grows only as \$O(ln\textbackslashensuremath\{\textbackslashbeta\})\$ for fermions and converges to a constant for bosons as temperature \$T=1/\textbackslashensuremath\{\textbackslashbeta\}\$ decreases. Third, we show that this remarkable feature is ascribed to the properties of the physically constructed basis functions. The fermionic basis functions on the real-frequency axis have features whose width is scaled as \$O(T)\$, which is consistent with the low-\$T\$ properties of quasiparticles in a Fermi liquid state. On the other hand, the properties of the bosonic basis functions are consistent with those of spin/orbital susceptibilities at low \$T\$. These results demonstrate the potential wide applications of the IR to calculations of correlated systems.}}, 
pages = {035104}, 
number = {3}, 
volume = {98}, 
language = {English}, 
month = {07}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Chikano-2018-Physical%20Review%20B.pdf}
}
@article{Shinaoka:2018cg, 
year = {2018}, 
rating = {0}, 
title = {{Overcomplete compact representation of two-particle Green's functions}}, 
author = {Shinaoka, Hiroshi and Otsuki, Junya and Haule, Kristjan and Wallerberger, Markus and Gull, Emanuel and Yoshimi, Kazuyoshi and Ohzeki, Masayuki}, 
journal = {Physical Review B}, 
doi = {10.1103/physrevb.97.205111}, 
url = {https://journals.aps.org/prb/pdf/10.1103/PhysRevB.97.205111}, 
abstract = {{Phys. Rev. B 97, 205111 (2018). doi:10.1103/PhysRevB.97.205111}}, 
pages = {205111}, 
number = {20}, 
volume = {97}, 
language = {English}, 
month = {05}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Shinaoka-2018-Physical%20Review%20B.pdf}
}
@article{irbasis2019, 
year = {2018}, 
rating = {0}, 
title = {{irbasis: Open-source database and software for intermediate-representation basis functions of imaginary-time Green’s function}}, 
author = {Chikano, Naoya and Yoshimi, Kazuyoshi and Otsuki, Junya and Shinaoka, Hiroshi}, 
journal = {Computer Physics Communications}, 
doi = {10.1016/j.cpc.2019.02.006}, 
eprint = {1807.05237}, 
url = {https://www.sciencedirect.com/science/article/pii/S001046551930058X?via\%3Dihub}, 
abstract = {{The open-source library, irbasis, provides easy-to-use tools for two sets of orthogonal functions named intermediate representation (IR). The IR basis enables a compact representation of the Matsubara Green's function and efficient calculations of quantum models. The IR basis functions are defined as the solution of an integral equation whose analytical solution is not available for this moment. The library consists of a database of pre-computed high-precision numerical solutions and computational code for evaluating the functions from the database. This paper describes technical details and demonstrates how to use the library.}}, 
journaltitle = {irbasis: Open-source database and software for intermediate-representation basis functions of imaginary-time Green’s function}, 
pages = {181--188}, 
volume = {240}, 
language = {English}, 
keywords = {}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Chikano-2018-Computer%20Physics%20Communications.pdf}
}
@article{EGull2018, 
year = {2018}, 
rating = {0}, 
title = {{Chebyshev polynomial representation of imaginary-time response functions}}, 
author = {Gull, Emanuel and Iskakov, Sergei and Krivenko, Igor and Rusakov, Alexander A and Zgid, Dominika}, 
journal = {Physical Review B}, 
doi = {10.1103/physrevb.98.075127}, 
eprint = {1805.03521}, 
abstract = {{Problems of finite-temperature quantum statistical mechanics can be formulated in terms of imaginary (Euclidean) -time Green's functions and self-energies. In the context of realistic Hamiltonians, the large energy scale of the Hamiltonian (as compared to temperature) necessitates a very precise representation of these functions. In this paper, we explore the representation of Green's functions and self-energies in terms of a series of Chebyshev polynomials. We show that many operations, including convolutions, Fourier transforms, and the solution of the Dyson equation, can straightforwardly be expressed in terms of the series expansion coefficients. We then compare the accuracy of the Chebyshev representation for realistic systems with the uniform-power grid representation, which is most commonly used in this context. 
Published in: Phys. Rev. B 98, 075127 (2018)}}, 
pages = {075127}, 
number = {7}, 
volume = {98}, 
language = {English}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Gull-Chebyshev%20polynomial%20representation%20of%20imaginary-time%20response%20functions-2018-Physical%20Review%20B.pdf}
}
@article{Otsuki:2017er, 
year = {2017}, 
rating = {0}, 
title = {{Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data}}, 
author = {Otsuki, Junya and Ohzeki, Masayuki and Shinaoka, Hiroshi and Yoshimi, Kazuyoshi}, 
journal = {Physical Review E}, 
doi = {10.1103/physreve.95.061302}, 
url = {https://journals.aps.org/pre/pdf/10.1103/PhysRevE.95.061302}, 
abstract = {{A data-science approach to solving the ill-conditioned inverse problem for analytical continuation is proposed. The root of the problem lies in the fact that even tiny noise of imaginary-time input data has a serious impact on the inferred real-frequency spectra. By means of a modern regularization technique, we eliminate redundant degrees of freedom that essentially carry the noise, leaving only relevant information unaffected by the noise. The resultant spectrum is represented with minimal bases and thus a stable analytical continuation is achieved. This framework further provides a tool for analyzing to what extent the Monte Carlo data need to be accurate to resolve details of an expected spectral function.}}, 
pages = {061302(R)}, 
number = {6}, 
volume = {95}, 
language = {English}, 
month = {06}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Otsuki-Sparse%20modeling%20approach%20to%20analytical%20continuation%20of%20imaginary-time%20quantum%20Monte%20Carlo%20data-2017-Physical%20Review%20E.pdf}
}
@article{Shinaoka:2017ix, 
year = {2017}, 
rating = {0}, 
title = {{Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains}}, 
author = {Shinaoka, Hiroshi and Otsuki, Junya and Ohzeki, Masayuki and Yoshimi, Kazuyoshi}, 
journal = {Physical Review B}, 
doi = {10.1103/physrevb.96.035147}, 
url = {https://journals.aps.org/prb/pdf/10.1103/PhysRevB.96.035147}, 
abstract = {{Model-independent compact representations of imaginary-time data are presented in terms of the intermediate representation (IR) of analytical continuation. We demonstrate the efficiency of the IR through continuous-time quantum Monte Carlo calculations of an Anderson impurity model. We find that the IR yields a significantly compact form of various types of correlation functions. This allows the direct quantum Monte Carlo measurement of Green's functions in a compressed form, which considerably reduces the computational cost and memory usage. Furthermore, the present framework will provide general ways to boost the power of cutting-edge diagrammatic/quantum Monte Carlo treatments of many-body systems.}}, 
pages = {035147 -- 8}, 
number = {3}, 
volume = {96}, 
language = {English}, 
month = {07}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Shinaoka-Compressing%20Green's%20function%20using%20intermediate%20representation%20between%20imaginary-time%20and%20real-frequency%20domains-2017-Physical%20Review%20B.pdf}
}
@article{Kananenka:2016cfa, 
year = {2016}, 
rating = {0}, 
title = {{Efficient Temperature-Dependent Green’s Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms}}, 
author = {Kananenka, Alexei A and Phillips, Jordan J and Zgid, Dominika}, 
journal = {Journal of Chemical Theory and Computation}, 
doi = {10.1021/acs.jctc.5b00884}, 
url = {http://pubs.acs.org/doi/pdf/10.1021/acs.jctc.5b00884}, 
pages = {564 -- 571}, 
number = {2}, 
volume = {12}, 
language = {English}, 
month = {02}
}
@article{Kaltak:2014ku, 
year = {2014}, 
rating = {0}, 
title = {{Low Scaling Algorithms for the Random Phase Approximation: Imaginary Time and Laplace Transformations}}, 
author = {Kaltak, Merzuk and Klimeš, Jiří and Kresse, Georg}, 
journal = {Journal of Chemical Theory and Computation}, 
issn = {1549-9618}, 
doi = {10.1021/ct5001268}, 
pmid = {26580770}, 
url = {http://pubs.acs.org/doi/pdfplus/10.1021/ct5001268}, 
pages = {2498 -- 2507}, 
number = {6}, 
volume = {10}, 
language = {English}, 
month = {05}
}
@article{Boehnke:2011dd, 
year = {2011-08}, 
rating = {0}, 
title = {{Orthogonal polynomial representation of imaginary-time Green’s functions}}, 
author = {Boehnke, Lewin and Hafermann, Hartmut and Ferrero, Michel and Lechermann, Frank and Parcollet, Olivier}, 
journal = {Physical Review B}, 
doi = {10.1103/physrevb.84.075145}, 
pages = {075145}, 
number = {7}, 
volume = {84}, 
language = {English}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Boehnke-Orthogonal%20polynomial%20representation%20of%20imaginary-time%20Green’s%20functions-2011-Physical%20Review%20B.pdf}
}
@article{Gull:2011jda, 
year = {2011-05}, 
rating = {2}, 
title = {{Continuous-time Monte Carlo methods for quantum impurity models}}, 
author = {Gull, Emanuel and Millis, Andrew J and Lichtenstein, Alexander I and Rubtsov, Alexey N and Troyer, Matthias and Werner, Philipp}, 
journal = {Reviews of Modern Physics}, 
issn = {0034-6861}, 
doi = {10.1103/revmodphys.83.349}, 
abstract = {{Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of “correlated electron” materials as auxiliary problems whose solution gives the “dynamical mean-field” approximation to the self-energy and local correlation functions. These applications require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms reviewed in this article meet this challenge. Derivations and descriptions of the algorithms are presented in enough detail to allow other workers to write their own implementations, discuss the strengths and weaknesses of the methods, summarize the problems to which the new methods have been successfully applied, and outline prospects for future applications.}}, 
pages = {349 -- 404}, 
number = {2}, 
volume = {83}, 
language = {English}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Gull-Continuous-time%20Monte Carlo%20methods%20for%20quantum%20impurity%20models-2011-Reviews%20of%20Modern%20Physics.pdf}
}
@article{Rubtsov:2008cs, 
year = {2008}, 
rating = {0}, 
title = {{Dual fermion approach to nonlocal correlations in the Hubbard model}}, 
author = {Rubtsov, A N and Katsnelson, M I and Lichtenstein, A I}, 
journal = {Physical Review B}, 
doi = {10.1103/physrevb.77.033101}, 
pages = {033101 -- 4}, 
number = {3}, 
volume = {77}, 
language = {English}, 
month = {01}
}
@article{Toschi:2007fq, 
year = {2007-01}, 
rating = {0}, 
title = {{Dynamical vertex approximation: A step beyond dynamical mean-field theory}}, 
author = {Toschi, A and Katanin, A and Held, K}, 
journal = {Physical Review B}, 
doi = {10.1103/physrevb.75.045118}, 
url = {http://journals.aps.org/prb/pdf/10.1103/PhysRevB.75.045118}, 
pages = {045118 -- 8}, 
number = {4}, 
volume = {75}, 
language = {English}
}
@article{Georges:1996un, 
year = {1996-01}, 
rating = {0}, 
title = {{Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions}}, 
author = {Georges, A and Kotliar, G and Krauth, W and Rozenberg, M J}, 
journal = {Reviews of Modern Physics}, 
doi = {10.1103/revmodphys.68.13}, 
abstract = {{We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.}}, 
pages = {13 -- 125}, 
number = {1}, 
volume = {68}, 
language = {English}, 
local-url = {file://localhost/Users/hiroshi/Documents/Papers%20Library/Georges-Dynamical%20mean-field%20theory%20of%20strongly%20correlated%20fermion%20systems%20and%20the%20limit%20of%20infinite%20dimensions-1996-Reviews%20of%20Modern%20Physics.pdf}
}
@article{Rojas:1995jd, 
year = {1995}, 
rating = {0}, 
title = {{Space-time method for ab initio calculations of self-energies and dielectric response functions of solids}}, 
author = {Rojas, H N and Godby, R W and Needs, R J}, 
journal = {Physical Review Letters}, 
doi = {10.1103/physrevlett.74.1827}, 
abstract = {{Abstract We present a new method for efficient, accurate calculations of many-body properties of periodic systems. The main features are (i) use of a real- space /imaginary- time representation,(ii) avoidance of any model form for the screened interaction W,(iii) exact ...}}, 
pages = {1827 -- 1830}, 
number = {10}, 
volume = {74}, 
language = {English}
}
@article{Gallicchio.1994.Berne, 
year = {1994}, 
title = {{The absorption spectrum of the solvated electron in fluid helium by maximum entropy inversion of imaginary time correlation functions from path integral Monte Carlo simulations}}, 
author = {Gallicchio, E and Berne, B J}, 
journal = {The Journal of Chemical Physics}, 
issn = {0021-9606}, 
doi = {10.1063/1.467892}, 
pages = {9909--9918}, 
number = {11}, 
volume = {101}
}
@article{Bickers.1991.White, 
year = {1991}, 
title = {{Conserving approximations for strongly fluctuating electron systems. II. Numerical results and parquet extension}}, 
author = {Bickers, N. E. and White, S. R.}, 
journal = {Physical Review B}, 
issn = {1098-0121}, 
doi = {10.1103/physrevb.43.8044}, 
pmid = {9996429}, 
abstract = {{We describe an iterative technique for solution of the de Dominicis–Martin parquet equations for lattice electrons and state the relationship of this approach to conserving extensions of Hartree-Fock theory. We propose a physically motivated and computationally feasible pseudopotential approximation, which allows the solution of the parquet equations for the two-dimensional Hubbard model. We present calculations of static and dynamic Hubbard-model correlation functions based on the pseudopotential parquet and a simpler conserving approximation. For a wide parameter range the pseudopotential parquet results are in nearly quantitative agreement with finite-lattice quantum Monte Carlo results.}}, 
pages = {8044--8064}, 
number = {10}, 
volume = {43}
}
@article{Bickers:1989hk, 
year = {1989}, 
rating = {0}, 
title = {{Conserving approximations for strongly fluctuating electron systems. I. Formalism and calculational approach}}, 
author = {Bickers, N E and Scalapino, D J}, 
journal = {Annals of Physics}, 
doi = {10.1016/0003-4916(89)90359-x}, 
abstract = {{Abstract We discuss the solution of nontrivial conserving approximations for electronic correlation functions in systems with strong collective fluctuations. The formal properties of conserving approximations have been well known for over twenty years, but numerical solutions have been limited to Hartree-Fock level. We extend the formal analysis of Baym and Kadanoff in order to derive the simplest self-consistent approximation based on ...}}, 
pages = {206 -- 251}, 
number = {1}, 
volume = {193}, 
language = {English}
}
@book{Hansen,
author = {Per Christian Hansen},
title = {Discrete Inverse Problems: Insights and Algorithms},
isbn = {978-0-898716-96-2},
publisher = {SIAM},
city = {Philadelphia},
year = {2010},
doi = {10.1137/1.9780898718836},
}
@book{Karlin,
author = {Samuel Karlin},
title = {Total Positivity},
isbn = {978-0804703147},
publisher = {Stanford University Press},
year = {1968}
}

@article{PhysRevB.90.054115,
  title = {Cubic scaling algorithm for the random phase approximation: Self-interstitials and vacancies in Si},
  author = {Kaltak, Merzuk and Klime\ifmmode \check{s}\else \v{s}\fi{}, Ji\ifmmode \check{r}\else \v{r}\fi{}\'{\i} and Kresse, Georg},
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  doi = {10.1103/PhysRevB.90.054115},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.90.054115}
}


@article{PhysRevB.94.165109,
  title = {Cubic scaling $GW$: Towards fast quasiparticle calculations},
  author = {Liu, Peitao and Kaltak, Merzuk and Klime\ifmmode \check{s}\else \v{s}\fi{}, Ji\ifmmode \check{r}\else \v{r}\fi{}\'{\i} and Kresse, Georg},
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  numpages = {13},
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  doi = {10.1103/PhysRevB.94.165109},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.94.165109}
}

@article{Bickers89a,
  title = {Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salpeter Equation and Dynamics for the Two-Dimensional Hubbard Model},
  author = {Bickers, N. E. and Scalapino, D. J. and White, S. R.},
  journal = {Phys. Rev. Lett.},
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  issue = {8},
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  doi = {10.1103/PhysRevLett.62.961},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.62.961}
}


@article{Bickers89b,
title = {Conserving approximations for strongly fluctuating electron systems. I. Formalism and calculational approach},
journal = {Annals of Physics},
volume = {193},
number = {1},
pages = {206-251},
year = {1989},
issn = {0003-4916},
doi = {https://doi.org/10.1016/0003-4916(89)90359-X},
url = {https://www.sciencedirect.com/science/article/pii/000349168990359X},
author = {N.E Bickers and D.J Scalapino},
abstract = {We discuss the solution of nontrivial conserving approximations for electronic correlation functions in systems with strong collective fluctuations. The formal properties of conserving approximations have been well known for over twenty years, but numerical solutions have been limited to Hartree-Fock level. We extend the formal analysis of Baym and Kadanoff in order to derive the simplest self-consistent approximation based on exchange of fluctuations in the particle-hole and particle-particle channels. We then describe a practical technique for calculating self-consistent single-particle Green's functions and solving the finite-temperature Bethe-Salpeter equation for electrons on a lattice.}
}

@article{Witt21,
  title = {Efficient fluctuation-exchange approach to low-temperature spin fluctuations and superconductivity: From the Hubbard model to ${\mathrm{Na}}_{x}{\mathrm{CoO}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}{y\mathrm{H}}_{2}\mathrm{O}$},
  author = {Witt, Niklas and van Loon, Erik G. C. P. and Nomoto, Takuya and Arita, Ryotaro and Wehling, Tim O.},
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  url = {https://link.aps.org/doi/10.1103/PhysRevB.103.205148}
}


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  author    = {N. F. Berk and J. R. Schrieffer},
  journal   = {Physical Review Letters},
  title     = {Effect of {F}erromagnetic {S}pin {C}orrelations on {S}uperconductivity},
  year      = {1966},
  month     = {aug},
  number    = {8},
  pages     = {433--435},
  volume    = {17},
  comment   = {Berk-Schrieffer interaction},
  doi       = {10.1103/physrevlett.17.433},
  publisher = {American Physical Society ({APS})},
  url       = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.17.433},
}

@article{Arita00,
author = {Arita ,Ryotaro and Kuroki ,Kazuhiko and Aoki ,Hideo},
title = {d- and p-Wave Superconductivity Mediated by Spin Fluctuations in Two- and Three-Dimensional Single-Band Repulsive Hubbard Model},
journal = {Journal of the Physical Society of Japan},
volume = {69},
number = {4},
pages = {1181-1191},
year = {2000},
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URL = {https://doi.org/10.1143/JPSJ.69.1181 },
eprint = {https://doi.org/10.1143/JPSJ.69.1181 }
}

@Article{Vilk1997,
  author        = {Y. M. Vilk and A.-M. S. Tremblay},
  journal       = {Journal de Physique I},
  title         = {Non-{P}erturbative {M}any-{B}ody {A}pproach to the {H}ubbard {M}odel and {S}ingle-{P}article {P}seudogap},
  year          = {1997},
  month         = {nov},
  number        = {11},
  pages         = {1309--1368},
  volume        = {7},
  archiveprefix = {arXiv},
  doi           = {10.1051/jp1:1997135},
  eprint        = {cond-mat/9702188},
  publisher     = {{EDP} Sciences},
}

@Inbook{Tremblay2012,
author="Tremblay, Andr{\'e}-Marie S.",
editor="Avella, Adolfo
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bookTitle="Strongly Correlated Systems: Theoretical Methods",
year="2012",
publisher="Springer Berlin Heidelberg",
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pages="409--453",
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doi="10.1007/978-3-642-21831-6_13",
url="https://doi.org/10.1007/978-3-642-21831-6_13",
archiveprefix = {arXiv},
eprint        = {1107.1534},
}

@Inbook{Allen2004,
  author        = {S. Allen and A.-M. S. Tremblay and Y. M. Vilk},
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  title         = {Conserving {A}pproximations vs. {T}wo-{P}article {S}elf-{C}onsistent {A}pproach},
  year          = {2004},
  editor        = {David Sénéchal and André-Marie Tremblay and Claude Bourbonnais},
  publisher     = {Springer-Verlag New York},
  archiveprefix = {arxiv},
  chapter       = {8},
  eprint        = {cond-mat/0110130},
  groups        = {Conserving approximation, TPSC},
}


@article{Zantout2021,
author = {Zantout, Karim and Backes, Steffen and Valentí, Roser},
title = {Two-Particle Self-Consistent Method for the Multi-Orbital Hubbard Model},
journal = {Annalen der Physik},
volume = {533},
number = {2},
pages = {2000399},
keywords = {correlated electrons, multi-orbital Hubbard model, non-perturbative methods},
doi = {https://doi.org/10.1002/andp.202000399},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.202000399},
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}

@article{Moukouri2000,
  title = {Many-body theory versus simulations for the pseudogap in the Hubbard model},
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@article{DLR,
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@misc{scipostreview,
  doi = {10.48550/ARXIV.2106.12685},
  url = {https://arxiv.org/abs/2106.12685},
  author = {Shinaoka, Hiroshi and Chikano, Naoya and Gull, Emanuel and Li, Jia and Nomoto, Takuya and Otsuki, Junya and Wallerberger, Markus and Wang, Tianchun and Yoshimi, Kazuyoshi},
  keywords = {Strongly Correlated Electrons (cond-mat.str-el), Materials Science (cond-mat.mtrl-sci), Superconductivity (cond-mat.supr-con), Computational Physics (physics.comp-ph), FOS: Physical sciences, FOS: Physical sciences},
  title = {Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function},
  publisher = {arXiv},
  year = {2021},
  copyright = {Creative Commons Zero v1.0 Universal}
}