Variational matrix product state approach to quantum impurity models

TL;DR

This paper introduces a unified matrix product state framework for quantum impurity models, enhancing computational efficiency and spectral analysis capabilities, especially for time-dependent and out-of-equilibrium problems.

Contribution

It unifies renormalization group methods within matrix product states and develops a variational approach for Green's functions, improving flexibility and efficiency.

Findings

Enhanced spectral property description at finite frequencies.

Improved computational efficiency, potentially linear scaling for multi-channel problems.

Successful application to the one-channel Kondo model.

Abstract

We present a unified framework for renormalization group methods, including Wilson's numerical renormalization group (NRG) and White's density-matrix renormalization group (DMRG), within the language of matrix product states. This allows improvements over Wilson's NRG for quantum impurity models, as we illustrate for the one-channel Kondo model. Moreover, we use a variational method for evaluating Green's functions. The proposed method is more flexible in its description of spectral properties at finite frequencies, opening the way to time-dependent, out-of-equilibrium impurity problems. It also substantially improves computational efficiency for one-channel impurity problems, suggesting potentially \emph{linear} scaling of complexity for $n$-channel problems.