Quantum transitions of the XY model with long-range interactions on the inhomogenous periodic chain

TL;DR

This paper exactly solves an inhomogeneous long-range XY spin chain model, revealing multiple quantum phase transitions induced by a transverse field, with detailed analysis of magnetization and susceptibility at zero temperature.

Contribution

It introduces an exact solution for the inhomogeneous long-range XY model on a periodic chain, extending previous models and analyzing quantum phase transitions in detail.

Findings

Multiple first- and second-order quantum transitions identified.

Phase diagrams mapped in the space of field and interaction parameters.

Detailed zero-temperature magnetization and susceptibility results provided.

Abstract

The isotropic XY model $(s=1/2)$ in a transverse field, with uniform long-range interactions among the transverse components of the spins, on the inhomogeneous periodic chain, is studied. The model, composed of $N$ segments with $n$ different exchange interactions and magnetic moments, is exactly solved by introducing the integral gaussian transformation and the generalized Jordan-Wigner transformation, which reduce the problem to the diagonalization of a finite matrix of $n$th order. The quantum transitions induced by the transverse field are determined by analyzing the induced magnetization of the cell and the equation of state. The phase diagrams for the quantum transitions, in the space generated by the transverse field and the interaction parameters, are presented. As expected, the model presents multiple, first- and second-order quantum transitions induced by the transverse field, and it corresponds to an extension of the models recently considered by the authors. Detailed results are also presented, at T=0, for the induced magnetization and isothermal susceptibility $\chi_{T}^{zz}$ as function of the transverse field.