Variational matrix product ansatz for dispersion relations

TL;DR

This paper introduces a variational matrix product state approach for calculating dispersion relations in quantum spin chains, efficiently handling topologically non-trivial states and demonstrating high accuracy in benchmark models.

Contribution

It presents a novel variational ansatz that works directly in the thermodynamic limit, including topologically non-trivial states, with efficient implementation for dispersion calculations.

Findings

Accurately reproduces known dispersion relations in benchmark models

Handles topologically non-trivial states such as kinks and domain walls

Achieves cubic scaling in bond dimension for efficiency

Abstract

A variational ansatz for momentum eigenstates of translation invariant quantum spin chains is formulated. The matrix product state ansatz works directly in the thermodynamic limit and allows for an efficient implementation (cubic scaling in the bond dimension) of the variational principle. Unlike previous approaches, the ansatz includes topologically non-trivial states (kinks, domain walls) for systems with symmetry breaking. The method is benchmarked using the spin-1/2 XXZ antiferromagnet and the spin-1 Heisenberg antiferromagnet and we obtain surprisingly accurate results.