String-charge duality in integrable lattice models

TL;DR

This paper establishes a direct link between the spectra of conserved operators and particle densities in integrable lattice models, exemplified by the XXZ spin chain, with applications to quantum quenches and efficient computational techniques.

Contribution

It introduces an explicit mapping between conserved spectra and particle densities in integrable models, including analytic solutions for specific states without relying on entropy principles.

Findings

Derived an explicit spectrum-density mapping for the XXZ chain

Developed an efficient implementation method for quantum quenches

Obtained analytic solutions for simple product states

Abstract

We derive an explicit mapping between the spectra of conserved local operators of integrable quantum lattice models and the density distributions of their thermodynamic particle content. This is presented explicitly for the Heisenberg XXZ spin chain. As an application we discuss a quantum quench scenario, in both the gapped and critical regimes. We outline an exact technique which allows for an efficient implementation on periodic matrix product states. In addition, for certain simple product states we obtain analytic closed-form expressions in terms of solutions to Hirota functional relations. Remarkably, no reference to a maximal entropy principle is invoked.