Converting long-range entanglement into mixture: tensor-network approach to local equilibration

TL;DR

This paper introduces a tensor network method that converts long-range entanglement into a mixture, enabling efficient local state representation during out-of-equilibrium quantum dynamics.

Contribution

The authors develop a novel tensor network approach to identify and transform long-range entanglement into a mixture, simplifying the simulation of quantum systems after a quench.

Findings

Efficient representation of long-time local states as density matrices.

Captures long-time behavior of local observables with limited computational resources.

Provides a new tool for studying local equilibration in quantum many-body systems.

Abstract

In the out-of-equilibrium evolution induced by a quench, fast degrees of freedom generate long-range entanglement that is hard to encode with standard tensor networks. However, local observables only sense such long-range correlations through their contribution to the reduced local state as a mixture. We present a tensor network method that identifies such long-range entanglement and efficiently transforms it into mixture, much easier to represent. In this way, we obtain an effective description of the time-evolved state as a density matrix that captures the long-time behavior of local operators with finite computational resources.