Efficient DMFT impurity solver using real-time dynamics with Matrix Product States

TL;DR

This paper introduces a novel method using Matrix Product States and TEBD to calculate spectral functions in quantum impurity models, enhancing resolution and revealing detailed spectral features within DMFT.

Contribution

It develops a real-time dynamics approach with linear prediction for impurity solvers in DMFT, demonstrating improved spectral resolution and detailed spectral features in Hubbard models.

Findings

Sharp features at Hubbard band edges persist in the thermodynamic limit.

Long-lived oscillations indicate coherent superpositions related to the Kondo peak.

Rich spectral structures observed in two-band Hubbard models.

Abstract

We propose to calculate spectral functions of quantum impurity models using the Time Evolving Block Decimation (TEBD) for Matrix Product States. The resolution of the spectral function is improved by a so-called linear prediction approach. We apply the method as an impurity solver within the Dynamical Mean Field Theory (DMFT) for the single- and two-band Hubbard model on the Bethe lattice. For the single-band model we observe sharp features at the inner edges of the Hubbard bands. A finite size scaling shows that they remain present in the thermodynamic limit. We analyze the real time-dependence of the double occupation after adding a single electron and observe oscillations at the same energy as the sharp feature in the Hubbard band, indicating a long-lived coherent superposition of states that correspond to the Kondo peak and the side peaks. For a two-band Hubbard model we observe an even richer structure in the Hubbard bands, which cannot be related to a multiplet structure of the impurity, in addition to sharp excitations at the band edges of a type similar to the single-band case.