Isolated Eigenvalues of the Ferromagnetic Spin-J XXZ Chain with Kink Boundary Conditions

TL;DR

This paper analyzes the spectral properties of the ferromagnetic spin-J XXZ chain with kink boundary conditions, demonstrating a spectral gap for J≥ 3/2 and the existence of a finite excitation gap in the thermodynamic limit.

Contribution

It proves the existence of a spectral gap for the lowest excited states in the spin-J XXZ chain with kink boundary conditions for J≥ 3/2.

Findings

Spectral gap exists for J≥ 3/2.

Finite number of excitations above ground state.

Gap persists in the thermodynamic limit.

Abstract

We investigate the low-lying excited states of the spin J ferromagnetic XXZ chain with Ising anisotropy Delta and kink boundary conditions. Since the third component of the total magnetization, M, is conserved, it is meaningful to study the spectrum for each fixed value of M. We prove that for J>= 3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum, uniformly in the length of the chain. In the thermodynamic limit, this means that there are a positive number of excitations above the ground state and below the essential spectrum.