Scattering particles in quantum spin chains

TL;DR

This paper introduces a variational, matrix product state-based method to analyze low-energy excitations in quantum spin chains, enabling detailed characterization of particles, interactions, and spectra in these systems.

Contribution

It develops a novel framework for describing excitations as particles with specific properties and interactions, applied to the Heisenberg antiferromagnetic ladder.

Findings

Computed elementary excitation spectrum of the ladder

Determined magnon-magnon S matrix and bound states

Analyzed static and dynamic properties of the magnetized system

Abstract

A variational approach for constructing an effective particle description of the low-energy physics of one-dimensional quantum spin chains is presented. Based on the matrix product state formalism, we compute the one- and two-particle excitations as eigenstates of the full microscopic Hamiltonian. We interpret the excitations as particles on a strongly-correlated background with non-trivial dispersion relations, spectral weights and two-particle S matrices. Based on this information, we show how to describe a finite density of excitations as an interacting gas of bosons, using its approximate integrability at low densities. We apply our framework to the Heisenberg antiferromagnetic ladder: we compute the elementary excitation spectrum and the magnon-magnon S matrix, study the formation of bound states and determine both static and dynamic properties of the magnetized ladder.