Quantum Phase Transition in the One-Dimensional XZ Model

TL;DR

This paper introduces a 1D XZ model with alternating interactions, providing exact solutions and revealing a quantum phase transition characterized by discontinuous correlations and ground state degeneracy.

Contribution

The paper presents two exact solution methods for the 1D XZ model, bridging the Ising and quantum compass models, and analyzes its quantum phase transition.

Findings

Discontinuous pseudospin correlations at the transition

Highly degenerate ground state in the compass limit

Exact solutions via mapping and fermionic methods

Abstract

We introduce a one-dimensional (1D) XZ model with alternating $\sigma_i^z\sigma_{i+1}^z$ and $\sigma_i^x\sigma_{i+1}^x$ interactions on even/odd bonds, interpolating between the Ising model and the quantum compass model. We present two ways of its exact solution by: ($i$) mapping to the quantum Ising models, and ($ii$) using fermions with spin 1/2. In certain cases the nearest neighbor pseudospin correlations change discontinuously at the quantum phase transition, where one finds highly degenerate ground state of the 1D compass model.