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Discrete Lehmann representation of imaginary time Green's functions [article]

Jason Kaye and Kun Chen and Olivier Parcollet
2022 arXiv   pre-print
The discrete Lehmann representation of a particular imaginary time Green's function can be recovered by interpolation at a set of r imaginary time nodes.  ...  We present an efficient basis for imaginary time Green's functions based on a low rank decomposition of the spectral Lehmann representation.  ...  The Flatiron Institute is a division of the Simons Foundation.  ... 
arXiv:2107.13094v2 fatcat:yujqz2vfbfav7ecevol4mnzzla

libdlr: Efficient imaginary time calculations using the discrete Lehmann representation [article]

Jason Kaye and Kun Chen and Hugo U. R. Strand
2022 arXiv   pre-print
We introduce libdlr, a library implementing the recently introduced discrete Lehmann representation (DLR) of imaginary time Green's functions.  ...  The simplicity of the DLR makes it straightforward to incorporate into existing codes as a replacement for less efficient representations of imaginary time Green's functions, and libdlr is intended to  ...  The Flatiron Institute is a division of the Simons Foundation.  ... 
arXiv:2110.06765v2 fatcat:szzss7pd4zaivp74gvvzfe2dmu

Smooth self-energy in the exact-diagonalization-based dynamical mean-field theory: Intermediate-representation filtering approach [article]

Yuki Nagai, Hiroshi Shinaoka
2018 arXiv   pre-print
The present scheme is based on a recently proposed compact representation of imaginary-time Green's functions, the intermediate representation (IR).  ...  However, these spectra are spiky and strongly depend on the way to discretize a continuous bath (e.g., the number of the bath sites).  ...  The present method is based on the recently shown fact that the imaginarytime/Matsubara Green's functions are sparse at finite T : the imaginary-time/frequency dependence of these Green's functions can  ... 
arXiv:1806.10316v3 fatcat:73brsidwmveypjvmxrdm6e2gru

Efficient Compression Of The Environment Of An Open Quantum System [article]

Max Nusspickel, George H. Booth
2020 arXiv   pre-print
These resulting bath orbitals are designed to directly reproduce the system Green's function, not hybridization, which allows for consideration of the relevant system energy scales to optimally model.  ...  a discrete set of bath states, mimicking the open system as a larger closed problem.  ...  We note that other choices of kernel functions f are possible and in appendix VI B we discuss one such choice, which would match the Legendre representation of the imaginary time Green's function.  ... 
arXiv:2003.06062v2 fatcat:fd56esyenndchhssomttfra3qi

Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains

Hiroshi Shinaoka, Junya Otsuki, Masayuki Ohzeki, Kazuyoshi Yoshimi
2017 Physical review B  
New model-independent compact representations of imaginary-time data are presented in terms of the intermediate representation (IR) of analytical continuation.  ...  We find that the IR yields a significantly compact form of various types of correlation functions.  ...  One example is estimating the spectral function from imaginary-time Green's function computed in QMC simulations.  ... 
doi:10.1103/physrevb.96.035147 fatcat:ox7k7paeqbamfjoiohzgw5zyme

Page 934 of Mathematical Reviews Vol. 25, Issue 5 [page]

1963 Mathematical Reviews  
H. 4821 Explicit representation of discrete-symmetry operators in quantum theory of free fields. Rev. Modern Phys. 34 (1962), 215-226.  ...  The lectures continue with an interesting section on Green’s functions.  ... 

Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields

V. M. Turkowski, J. K. Freericks
2006 Physical Review B  
We derive exact operator average expressions for the first two spectral moments of nonequilibrium Green's functions for the Falicov-Kimball model and the Hubbard model in the presence of a spatially uniform  ...  We begin our formal developments with a derivation of exact expressions for the zeroth, first, and second spectral moments of the retarded and lesser Green's functions; the analysis is performed for the  ...  DMR-0210717 and by the Office of Naval Research under Grant No. N00014-05-1-0078. We would also like to thank the referees for comments that helped improve the manuscript.  ... 
doi:10.1103/physrevb.73.075108 fatcat:ynh7urcamzgtbbfhwxkwykq7vu

Sparse sampling approach to efficient ab initio calculations at finite temperature [article]

Jia Li, Markus Wallerberger, Naoya Chikano, Chia-Nan Yeh, Emanuel Gull, Hiroshi Shinaoka
2019 arXiv   pre-print
Efficient ab initio calculations of correlated materials at finite temperature require compact representations of the Green's functions both in imaginary time and Matsubara frequency.  ...  These sampling points accurately resolve the information contained in the Green's function, and efficient transforms between different representations are formulated with minimal loss of information.  ...  CONCLUSIONS We have introduced a sparse sampling scheme for imaginary-time Green's functions which greatly reduces the size of imaginary time and frequency grids in realistic calculations.  ... 
arXiv:1908.07575v1 fatcat:vk3rrnn3wjgfxd362yg7hrtupa

A fast time domain solver for the equilibrium Dyson equation [article]

Jason Kaye, Hugo U. R. Strand
2022 arXiv   pre-print
We consider the numerical solution of the real time equilibrium Dyson equation, which is used in calculations of the dynamical properties of quantum many-body systems.  ...  The resulting method can reach large propagation times, and is thus well-suited to explore quantum many-body phenomena at low energy scales.  ...  The Flatiron Institute is a division of the Simons Foundation.  ... 
arXiv:2110.06120v2 fatcat:lhxcb5sawra75gv2anigsvm7wi

Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function

Naoya Chikano, Junya Otsuki, Hiroshi Shinaoka
2018 Physical review B  
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.  ...  Intermediate representation of imaginary-time and real-frequency domains Definition of basis functions The IR basis is derived from the spectral (Lehmann) representation, which connects G α (τ ) with  ... 
doi:10.1103/physrevb.98.035104 fatcat:3x534343gfgdffatfdpxzqmezq

Structure of the Forward Scattering Amplitude

S. Deser, W. Gilbert, E. C. G. Sudarshan
1960 Physical Review  
The "bound-state" term is separated oG and related to the vertex functions. As a simple application, forward-scattering dispersion relations are derived by specialization of the Green's function.  ...  Use of the axioms of local Geld theory leads to an integral representation for the Fourier transform of matrix elements of the retarded commutator in terms of two invariant momentum parameters.  ...  We shall find that the integral representation of the time-ordered Green's function everywhere in the physical region can be deduced from that of the commutator matrix element, provided certain "stability  ... 
doi:10.1103/physrev.117.266 fatcat:fb5jrn5jpvdktn2g5jftzdiez4

irbasis: Open-source database and software for intermediate-representation basis functions of imaginary-time Green's function [article]

Naoya Chikano, Kazuyoshi Yoshimi, Junya Otsuki, Hiroshi Shinaoka
2019 arXiv   pre-print
The IR basis enables a compact representation of the Matsubara Green's function and efficient calculations of quantum models.  ...  The open-source library, irbasis, provides easy-to-use tools for two sets of orthogonal functions named intermediate representation (IR).  ...  Therefore, there is a high demand for a compact representation of the imaginary-time dependence of the Green's function in practical calculations.  ... 
arXiv:1807.05237v2 fatcat:frkzvkxbgvfzxjlkrfx5c3otfa

Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function [article]

Hiroshi Shinaoka, Naoya Chikano, Emanuel Gull, Jia Li, Takuya Nomoto, Junya Otsuki, Markus Wallerberger, Tianchun Wang, Kazuyoshi Yoshimi
2021 arXiv   pre-print
The sparse-modeling techniques are based on a compact orthogonal basis representation, intermediate representation (IR) basis functions, for imaginary-time and Matsubara Green's functions.  ...  This lecture note reviews recently proposed sparse-modeling approaches for efficient ab initio many-body calculations based on the data compression of Green's functions.  ...  Masayuki Ozeki, which aims to apply sparse modeling to quantum many-body calculations, led to the discovery of the IR basis.  ... 
arXiv:2106.12685v1 fatcat:7ngwpm3rqjberbhdgpeab2sayq

Elementary band representations for the single-particle Green's function of interacting topological insulators [article]

Dominik Lessnich, Stephen M. Winter, Mikel Iraola, Maia G. Vergniory, Roser Valentí
2021 arXiv   pre-print
We discuss the applicability of elementary band representations (EBRs) to diagnose spatial- and time-reversal-symmetry protected topological phases in interacting insulators in terms of their single-particle  ...  Green's functions.  ...  The time evolution is in imaginary time τ . T denotes time ordering in imaginary time and |0 denotes the ground state, which in the following we assume to be non-degenerate.  ... 
arXiv:2103.02624v1 fatcat:43ekuhr3vndjnkuy5ndco6xtf4

Distributional exact diagonalization formalism for quantum impurity models

Mats Granath, Hugo U. R. Strand
2012 Physical Review B  
The method enables calculation of the full analytic self-energy and single-particle Green's function in the complex frequency plane, without analytic continuation, and can be used for both finite and zero  ...  Results are in good agreement with imaginary frequency data from continuous-time quantum Monte Carlo calculations for the single impurity Anderson model and the two-orbital Hubbard model within dynamical  ...  The sampling of the thermal Green's function in imaginary time or frequency is very efficient but, statistical errors grow with decreased temperature.  ... 
doi:10.1103/physrevb.86.115111 fatcat:vyfjg52ftjch5hcxvrtetko23y
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