Simulating the out-of-equilibrium dynamics of local observables by trading entanglement for mixture

TL;DR

This paper introduces an algorithm that approximates the out-of-equilibrium dynamics of quantum systems by converting entanglement into mixture, enabling efficient simulation of local observables after a quantum quench.

Contribution

It proposes a novel method to trade entanglement for mixture, preserving local properties while reducing computational complexity in simulating quantum dynamics.

Findings

Algorithm accurately predicts local observables after quenches.

Benchmarking on quadratic Fermionic Hamiltonians shows effectiveness.

Method maintains local reduced density matrices during approximation.

Abstract

The fact that the computational cost of simulating a many-body quantum system on a computer increases with the amount of entanglement has been considered as the major bottleneck for simulating its out-of-equilibrium dynamics. Some aspects of the dynamics are, nevertheless, robust under appropriately devised approximations. Here we present a possible algorithm that allows to systematically approximate the equilibration value of local operators after a quantum quench. At the core of our proposal there is the idea to transform entanglement between distant parts of the system into mixture, and at the same time preserving the local reduced density matrices of the system. We benchmark the resulting algorithm by studying quenches of quadratic Fermionic Hamiltonians.