Dynamic properties of the spin-1/2 XY chain with three-site interactions

TL;DR

This paper analyzes the dynamic properties of a spin-1/2 XY chain with added three-site interactions, providing exact solutions and exploring how these interactions influence the system's excitation spectra and phases.

Contribution

It introduces a rigorous analysis of a spin chain model with three-site interactions using Jordan-Wigner transformation, revealing how these interactions affect dynamic structure factors and ground-state phases.

Findings

Closed-form expression for zz dynamic structure factor

Identification of features indicating three-site interactions

Analysis of two-fermion and many-fermion excitation continua

Abstract

We consider a spin-1/2 XY chain in a transverse (z) field with multi-site interactions. The additional terms introduced into the Hamiltonian involve products of spin components related to three adjacent sites. A Jordan-Wigner transformation leads to a simple bilinear Fermi form for the resulting Hamiltonian and hence the spin model admits a rigorous analysis. We point out the close relationships between several variants of the model which were discussed separately in previous studies. The ground-state phases (ferromagnet and two kinds of spin liquid) of the model are reflected in the dynamic structure factors of the spin chains, which are the main focus in this study. First we consider the zz dynamic structure factor reporting for this quantity a closed-form expression and analyzing the properties of the two-fermion (particle-hole) excitation continuum which governs the dynamics of transverse spin component fluctuations and of some other local operator fluctuations. Then we examine the xx dynamic structure factor which is governed by many-fermion excitations, reporting both analytical and numerical results. We discuss some easily recognized features of the dynamic structure factors which are signatures for the presence of the three-site interactions.