Particles, holes and solitons: a matrix product state approach

TL;DR

This paper presents a variational approach using continuous matrix product states to compute dispersion relations in 1+1D quantum field theories, successfully benchmarking against the Lieb-Liniger model and exploring non-integrable extensions.

Contribution

It introduces an efficient variational method based on continuous matrix product states for dispersion calculations in quantum field theories, including non-integrable models.

Findings

Excellent agreement with exact solutions for the Lieb-Liniger model

Identification of solitonic signatures in the excitation spectrum

Evidence of bound-state excitations in a non-integrable model

Abstract

We introduce a variational method for calculating dispersion relations of translation invariant (1+1)-dimensional quantum field theories. The method is based on continuous matrix product states and can be implemented efficiently. We study the critical Lieb-Liniger model as a benchmark and excelent agreement with the exact solution is found. Additionally, we observe solitonic signatures of Lieb's Type II excitation. In addition, a non-integrable model is introduced where a U(1)-symmetry breaking term is added to the Lieb-Liniger Hamiltonian. For this model we find evidence of a non-trivial bound-state excitation in the dispersion relation.