Comparison of MPS based real time evolution algorithms for Anderson Impurity Models

TL;DR

This paper compares two MPS-based algorithms for simulating Anderson Impurity Models, revealing that TEBD in star geometry offers superior efficiency and accuracy over TDVP in chain geometry, especially for large systems.

Contribution

It introduces an adapted TEBD algorithm for star geometry and systematically compares its performance with TDVP in chain geometry for impurity models.

Findings

TEBD in star geometry is faster and more accurate than TDVP in chain geometry.

Errors are generally independent of system size, except for TEBD in chain geometry.

The choice of bath representation and algorithm significantly affects simulation efficiency.

Abstract

We perform a detailed comparison of two Matrix Product States (MPS) based time evolution algorithms for Anderson Impurity Models. To describe the bath, we use both the star-geometry as well as the commonly employed Wilson chain geometry. For each bath geometry, we use either the Time Dependent Variational Principle (TDVP) or the Time Evolving Block Decimation (TEBD) to perform the time evolution. To apply TEBD for the star-geometry, we use a specially adapted algorithm that can deal with the long-range coupling terms. Analyzing the major sources of errors, one expects them to be proportional to the system size for all algorithms. Surprisingly, we find errors independent of system size except for TEBD in chain geometry. Additionally, we show that the right combination of bath representation and time evolution algorithm is important. While TDVP in chain geometry is a very precise approach, TEBD in star geometry is much faster, such that for a given accuracy it is superior to TDVP in chain geometry. This makes the adapted version of TEBD in star geometry the most efficient method to solve impurity problems.