Discrete Lehmann representation of imaginary time Green's functions

@article{Kaye2022DiscreteLR,
  title={Discrete Lehmann representation of imaginary time Green's functions},
  author={Jason Kaye and Kun Chen and Olivier Parcollet},
  journal={ArXiv},
  year={2022},
  volume={abs/2107.13094}
}
We present an efficient basis for imaginary time Green’s functions based on a low rank decomposition of the spectral Lehmann representation. The basis functions are simply a set of well-chosen exponentials, so the corresponding expansion may be thought of as a discrete form of the Lehmann representation using an effective spectral density which is a sum of δ functions. The basis is determined only by an upper bound on the product βωmax, with β the inverse temperature and ωmax an energy cutoff… 
View PDF on arXiv
View With Semantic Reader
6 Citations
Background Citations
1
Methods Citations
1

6 Citations

libdlr: Efficient imaginary time calculations using the discrete Lehmann representation
A fast time domain solver for the equilibrium Dyson equation
TLDR
This work proposes a quasilinear-scaling FFT-based algorithm which respects the structure of the nonlinear integral operator of Volterra integro-differential equations, and can reach large propagation times, and is thus wellsuited to explore quantum many-body phenomena at low energy scales.
Fully Self-Consistent Finite-Temperature $GW$ in Gaussian Bloch Orbitals for Solids
We present algorithmic and implementation details for the fully self-consistent finite-temperature GW method in Gaussian Bloch orbitals for solids. Our implementation is based on the…
sparse-ir: optimal compression and sparse sampling of many-body propagators
TLDR
Sparse-ir is introduced, a collection of libraries to handle imaginary-time propagators, a central object in quantum many-body calculations, and IR and sparse sampling are packaged into stand-alone, easy-to-use Python, Julia and Fortran libraries, which can readily be included into existing software.
Precise Low-Temperature Expansions for the Sachdev-Ye-Kitaev model
We solve numerically the large N Dyson-Schwinger equations for the Sachdev-Ye-Kitaev (SYK) model utilizing the Legendre polynomial decomposition and reaching 10 − 36 accuracy. Using this we compute…
Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function
TLDR
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 and describes a numerical library for the IR basis and the sparse sampling method, sparse-ir, and its sample codes.

References

SHOWING 1-10 OF 39 REFERENCES
Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function
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…
Orthogonal polynomial representation of imaginary-time Green’s functions
We study the expansion of single-particle and two-particle imaginary-time Matsubara Green's functions of quantum impurity models in the basis of Legendre orthogonal polynomials. We discuss various…
Chebyshev polynomial representation of imaginary-time response functions
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,…
Efficient Temperature-Dependent Green's Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms.
TLDR
This paper determines efficient imaginary time grids for the temperature-dependent Matsubara Green's function formalism that can be used for calculations on realistic systems and shows that only a limited number of orthogonal polynomial expansion coefficients are necessary to preserve accuracy.
Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
New model-independent compact representations of imaginary-time data are presented in terms of the intermediate representation (IR) of analytical continuation. This is motivated by a recent numerical…
Legendre-spectral Dyson equation solver with super-exponential convergence.
TLDR
A Legendre-spectral algorithm for solving the Dyson equation that inherits the known faster-than-exponential convergence of the Green's function's Legendre series expansion and allows for an energy accuracy of 10-9Eh with only a few hundred expansion coefficients.
Smooth Self-energy in the Exact-diagonalization-based Dynamical Mean-field Theory: Intermediate-representation Filtering Approach
We propose a method for obtaining converged smooth real-frequency self-energy as a function of a discretized bath number in the dynamical mean-field theory with the finite-temperature exact…
Overcomplete compact representation of two-particle Green's functions
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at…
Sparse sampling approach to efficient ab initio calculations at finite temperature
TLDR
A general procedure is introduced which generates sparse sampling points in time and frequency from compact orthogonal basis representations, such as Chebyshev polynomials and intermediate representation (IR) basis functions, which accurately resolve the information contained in the Green's function.
On approximation of functions by exponential sums
...
...