Variational Matrix Product Ansatz for Nonuniform Dynamics in the Thermodynamic Limit

TL;DR

This paper introduces a variational matrix product state approach for simulating nonuniform quantum dynamics directly in the thermodynamic limit, enabling efficient study of localized excitations.

Contribution

It presents a novel implementation of the time-dependent variational principle for matrix product states in infinite systems with localized nonuniformities.

Findings

Effective simulation of localized excitations in infinite systems.

Reduction of boundary reflection artifacts in nonuniform regions.

Application to spin-1 Heisenberg and $^4$ models.

Abstract

We describe how to implement the time-dependent variational principle for matrix product states in the thermodynamic limit for nonuniform lattice systems. This is achieved by confining the nonuniformity to a (dynamically growable) finite region with fixed boundary conditions. The suppression of unphysical quasiparticle reflections from the boundary of the nonuniform region is also discussed. Using this algorithm we study the dynamics of localized excitations in infinite systems, which we illustrate in the case of the spin-1 anti-ferromagnetic Heisenberg model and the $\phi^4$ model.