An Impurity Solver Using the Time-Dependent Variational Matrix Product State Approach

TL;DR

This paper employs the time-dependent variational matrix product state method to study the dynamical properties of the single impurity Anderson model, offering a new impurity solver approach for dynamical mean field theory with promising accuracy.

Contribution

The paper introduces a novel application of the tVMPS approach as an impurity solver for the SIAM, including finite temperature effects, and compares it with existing methods.

Findings

Accurately computes spectral functions of SIAM.

Demonstrates the effectiveness of tVMPS as an impurity solver.

Provides a comparison with Lanczos and quantum Monte Carlo methods.

Abstract

We use the time dependent variational matrix product state (tVMPS) approach to investigate the dynamical properties of the single impurity Anderson model (SIAM). Under the Jordan-Wigner transformation, the SIAM is reformulated into two spin-1/2 XY chains with local magnetic fields along the z-axis. The chains are connected by the longitudinal Ising coupling at the end points. The ground state of the model is searched variationally within the space spanned by the matrix product state (MPS). The temporal Green's functions are calculated both by the imaginary and real time evolutions, from which the spectral information can be extracted. The possibility of using the tVMPS approach as an impurity solver for the dynamical mean field theory is also addressed. Finite temperature density operator is obtained by the ancilla approach. The results are compared to those from the Lanczos and the Hirsch-Fye quantum Monte-Carlo methods.