Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench

TL;DR

This paper introduces an infinite Grassmann time-evolving matrix product operator method for quantum impurity problems after a quench, enabling efficient long-time non-equilibrium simulations with cost independent of evolution time.

Contribution

The authors develop a novel infinite matrix product state technique that handles non-equilibrium impurity dynamics post-quench with time-independent computational cost.

Findings

Method matches exact diagonalization results in integrable cases.

Outperforms existing approaches on the Kadanoff-Baym contour.

Potential for efficient long-time impurity simulations in non-equilibrium DMFT.

Abstract

An emergent numerical approach to solve quantum impurity problems is to encode the impurity path integral as a matrix product state. For time-dependent problems, the cost of this approach generally scales with the evolution time. Here we consider a common non-equilibrium scenario where an impurity, initially in equilibrium with a thermal bath, is driven out of equilibrium by a sudden quench of the impurity Hamiltonian. Despite that there is no time-translational invariance in the problem, we show that we could still make full use of the infinite matrix product state technique, resulting in a method whose cost is essentially independent of the evolution time. We demonstrate the effectiveness of this method in the integrable case against exact diagonalization, and against existing calculations on the L-shaped Kadanoff-Baym contour in the general case. Our method could be a very competitive method for studying long-time non-equilibrium quantum dynamics, and be potentially used as an efficient impurity solver in the non-equilibrium dynamical mean field theory.