Quantum phase transition in the one-dimensional compass model

TL;DR

This paper introduces a one-dimensional quantum model that interpolates between the Ising and compass models, revealing a first-order quantum phase transition characterized by discontinuous correlations and a highly degenerate disordered ground state.

Contribution

The paper provides an exact solution to a new interpolating model, demonstrating the nature of its quantum phase transition and ground state degeneracy.

Findings

Discontinuous change in nearest neighbor correlations.

Divergent correlation length at the transition.

Highly degenerate disordered ground state.

Abstract

We introduce a one-dimensional model which interpolates between the Ising model and the quantum compass model with frustrated pseudospin interactions $\sigma_i^z\sigma_{i+1}^z$ and $\sigma_i^x\sigma_{i+1}^x$, alternating between even/odd bonds, and present its exact solution by mapping to quantum Ising models. We show that the nearest neighbor pseudospin correlations change discontinuosly and indicate divergent correlation length at the first order quantum phase transition. At this transition one finds the disordered ground state of the compass model with high degeneracy $2\times 2^{N/2}$ in the limit of $N\to\infty$.