Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential

TL;DR

This paper investigates the use of the time-dependent variational principle within matrix product state manifolds for long-term quantum dynamics, highlighting both potential pitfalls and cases where it provides reliable results.

Contribution

It demonstrates the conditions under which the variational approach converges reliably for disordered nonintegrable systems and discusses the method's limitations for long time dynamics.

Findings

Long time observables convergence is subtle and system-dependent.

In disordered nonintegrable systems, the method agrees with known short time behavior.

Careful convergence analysis is essential for reliable long-term predictions.

Abstract

We study the applicability of the time-dependent variational principle in matrix product state manifolds for the long time description of quantum interacting systems. By studying integrable and nonintegrable systems for which the long time dynamics are known we demonstrate that convergence of long time observables is subtle and needs to be examined carefully. Remarkably, for the disordered nonintegrable system we consider the long time dynamics are in good agreement with the rigorously obtained short time behavior and with previous obtained numerically exact results, suggesting that at least in this case the apparent convergence of this approach is reliable. Our study indicates that while great care must be exercised in establishing the convergence of the method, it may still be asymptotically accurate for a class of disordered nonintegrable quantum systems.