libdlr: Efficient imaginary time calculations using the discrete Lehmann representation

Kaye, Jason; Chen, Kun; Strand, Hugo U. R.

doi:10.1016/j.cpc.2022.108458

Cited by 17 publications

(4 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…All numerical experiments were implemented in Fortran and carried out on a single CPU core of a laptop with an Intel Xeon E-2176 M 2.70GHz processor. The Fortran library libdlr was used for an implementation of the DLR [52] (https://github.com/ jasonkaye/libdlr). The FFTW library [53] was used for FFTs.…”

Section: Numerical Examplesmentioning

confidence: 99%

A fast time domain solver for the equilibrium Dyson equation

Kaye

Strand

2023

Adv Comput Math

Self Cite

View full text Add to dashboard Cite

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. We show that this equation can be written as a system of coupled, nonlinear, convolutional Volterra integro-differential equations, for which the kernel depends self-consistently on the solution. As is typical in the numerical solution of Volterra-type equations, the computational bottleneck is the quadratic-scaling cost of history integration. However, the structure of the nonlinear Volterra integral operator precludes the use of standard fast algorithms. We propose a quasilinear-scaling FFT-based algorithm which respects the structure of the nonlinear integral operator. The resulting method can reach large propagation times and is thus well-suited to explore quantum many-body phenomena at low energy scales. We demonstrate the solver with two standard model systems: the Bethe graph and the Sachdev-Ye-Kitaev model.

show abstract

Section: Numerical Examplesmentioning

confidence: 99%

A fast time domain solver for the equilibrium Dyson equation

Kaye

Strand

2023

Adv Comput Math

Self Cite

View full text Add to dashboard Cite

show abstract

“…The DMFT calculation is implemented using the TRIQS library [31], and the Python library pydlr provided by libdlr [16,32] is used for DLR calculations. We solve the DMFT equations at β = 232 eV −1 , which corresponds to T = 50 K. At this temperature, without the DLR, approximately 12000 Matsubara frequency nodes are required to adequately capture the slowly-decaying tail of the Green's functions to allow for accurate Fourier transforms.…”

Section: Numerical Example: Strontium Ruthenatementioning

confidence: 99%

“…They therefore yield exceptionally compact representations with controllable, high-order accuracy. Fortran, Python, and Julia libraries are available for both the IR with sparse sampling [15] and the DLR [16]. Low rank Green's function representations have been used to solve self-consistent diagrammatic equations in a variety of applications, including the SYK model [14,16,17], the self-consistent finite temperature GW method [13,18], Eliashberg-type equations for superconductivity [19][20][21][22], and Bethe-Salpeter-type equations for Hubbard models [23].…”

Section: Introductionmentioning

confidence: 99%

Low rank Green's function representations applied to dynamical mean-field theory

Sheng¹,

Hampel²,

Beck³

et al. 2023

Preprint

View full text Add to dashboard Cite

Several recent works have introduced highly compact representations of single-particle Green's functions in the imaginary time and Matsubara frequency domains, as well as efficient interpolation grids used to recover the representations. In particular, the intermediate representation with sparse sampling and the discrete Lehmann representation (DLR) make use of low rank compression techniques to obtain optimal approximations with controllable accuracy. We consider the use of the DLR in dynamical mean-field theory (DMFT) calculations, and in particular show that the standard full Matsubara frequency grid can be replaced by the compact grid of DLR Matsubara frequency nodes. We test the performance of the method for a DMFT calculation of Sr2RuO4 at temperature 50 K using a continuous-time quantum Monte Carlo impurity solver, and demonstrate that Matsubara frequency quantities can be represented on a grid of only 36 nodes with no reduction in accuracy, or increase in the number of self-consistent iterations, despite the presence of significant Monte Carlo noise.

show abstract

“…29,30 The hybridization function is implicitly included in Weiss Green's function, which could be implemented by using the discrete Lehmann representation (DLR) in the imaginary time and Matsubara frequency domains. 34 Then, the DLR scheme could be encoded into DMFT calculations, in which the standard full Matsubara frequency grid can be replaced by the grid of DLR Matsubara frequency nodes. 35 Finally, the self-energy could be derived from the Green's function through the CT-QMC impurity solver.…”

Section: Computational Detailsmentioning

confidence: 99%

Electron correlation and relativistic effects on the electronic properties of a plutonium and americium mixed oxide (PuAmO₄): from single-particle approximation to dynamical mean-field theory

Li,

Wang,

Liu

et al. 2023

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

show abstract

libdlr: Efficient imaginary time calculations using the discrete Lehmann representation

Cited by 17 publications

References 27 publications

A fast time domain solver for the equilibrium Dyson equation

A fast time domain solver for the equilibrium Dyson equation

Low rank Green's function representations applied to dynamical mean-field theory

Electron correlation and relativistic effects on the electronic properties of a plutonium and americium mixed oxide (PuAmO₄): from single-particle approximation to dynamical mean-field theory

Contact Info

Product

Resources

About

libdlr: Efficient imaginary time calculations using the discrete Lehmann representation

Cited by 17 publications

References 27 publications

A fast time domain solver for the equilibrium Dyson equation

A fast time domain solver for the equilibrium Dyson equation

Low rank Green's function representations applied to dynamical mean-field theory

Electron correlation and relativistic effects on the electronic properties of a plutonium and americium mixed oxide (PuAmO4): from single-particle approximation to dynamical mean-field theory

Contact Info

Product

Resources

About

Electron correlation and relativistic effects on the electronic properties of a plutonium and americium mixed oxide (PuAmO₄): from single-particle approximation to dynamical mean-field theory