Exiton, Spinon and Spin Wave Modes in an Exactly Soluble One-Dimensional Quantum Many-Body System

TL;DR

This paper provides an exact solution to a one-dimensional quantum many-body system with specific interactions, revealing detailed spectral properties and excitation modes, including excitons and spin waves, depending on the parameter s.

Contribution

It introduces a new exactly solvable model with distinct interaction potentials and analyzes its complete spectrum and excitation modes, expanding understanding of quantum many-body systems.

Findings

Exact solution for the spectrum and ground state.

Identification of exciton, spin wave, and continuum excitations.

Different excitation behaviors for s>0 and -1<s<0.

Abstract

In this paper, we present the exact solution to a one-dimensional, two-component, quantum many-body system in which like particles interact with a pair potential $s(s+1)/{\rm sinh}^{2}(r)$, while unlike particles interact with a pair potential $-s(s+1)/{\rm cosh}^{2}(r)$. We first give a proof of integrability, then derive the coupled equations determining the complete spectrum. All singularities occur in the ground state when there are equal numbers of the two components; we give explicit results for the ground state and low-lying states in this case. For $s>0$, the system is an antiferromagnet/insulator, with excitations consisting of a pair-hole--pair continuum, a two-particle continuum with gap, and excitons with gaps. For $-1<s<0$, the system has excitations consisting of a hole-particle continuum, and a two-spin wave continuum, both gap-less.