Quantum thermalization dynamics with Matrix-Product States

TL;DR

This paper demonstrates that tensor-network methods, specifically the time-dependent variational principle, can effectively simulate long-time thermalization dynamics in quantum systems, enabling extraction of transport properties despite entanglement growth.

Contribution

It shows that long-time local observable dynamics can be accurately captured with small bond dimensions, challenging the belief that entanglement growth limits such simulations.

Findings

Local observables are well approximated at long times

Transport coefficients like the energy diffusion constant can be extracted

Chaotic wavefront exhibits ballistic diffusively-broadening behavior

Abstract

We study the dynamics of thermalization following a quantum quench using tensor-network methods. Contrary to the common belief that the rapid growth of entanglement and the resulting exponential growth of the bond dimension restricts simulations to short times, we demonstrate that the long time limit of local observables can be well captured using the time-dependent variational principle. This allows to extract transport coefficients such as the energy diffusion constant from simulations with rather small bond dimensions. We further study the characteristic of the chaotic wave that precedes the emergence of hydrodynamics, to find a ballistic diffusively-broadening wave-front.