Performance of the time-dependent variational principle for matrix product states in long-time evolution of a pure state

TL;DR

This paper evaluates the effectiveness of the time-dependent variational principle (TDVP) with matrix product states for simulating long-time quantum dynamics, highlighting its strengths and limitations in conserving energy and accurately capturing observables.

Contribution

The study demonstrates that projecting TDVP improves long-time global observable behavior in nonintegrable models, providing insights into its advantages and drawbacks.

Findings

TDVP with projection enhances energy conservation during long-time evolution.

Global observables like kinetic and interaction energies are better captured by projected TDVP.

Errors in some observables can increase due to projection, compared to state truncation.

Abstract

The projection of time-dependent variational principle (TDVP) for matrix product states enables us to perform long-time simulations of one-dimensional quantum systems with the conservation of the total energy and the norm of wave functions. We compare long-time dynamics after a quantum quench simulated by TDVP with those by the exact diagonalization method in order to evaluate the performance of TDVP. We show that in a nonintegrable model the projection of TDVP clearly improves the long-time behaviors of global observables included in the Hamiltonian, such as the kinetic and interaction energies. In contrast, this projection can lead to larger error for other observables than that caused by the truncation of states.