Spontaneous symmetry breaking in a generalized orbital compass model

TL;DR

This paper studies a generalized orbital compass model, revealing a quantum phase transition driven by frustration, with insights from MERA and spin-wave theory about the nature of symmetry breaking and correlations.

Contribution

It introduces a continuous interpolation between Ising and orbital compass models and analyzes the quantum phase transition using advanced numerical and analytical methods.

Findings

Frustration induces a second order quantum phase transition.

Symmetry breaking occurs near maximally frustrated interactions.

Critical ground state lacks algebraically decaying spin-spin correlations.

Abstract

We introduce a generalized two-dimensional orbital compass model, which interpolates continuously from the classical Ising model to the orbital compass model with frustrated quantum interactions, and investigate it using the multiscale entanglement renormalization ansatz (MERA). The results demonstrate that increasing frustration of exchange interactions triggers a second order quantum phase transition to a degenerate symmetry broken state which minimizes one of the interactions in the orbital compass model. Using boson expansion within the spin-wave theory we unravel the physical mechanism of the symmetry breaking transition as promoted by weak quantum fluctuations and explain why this transition occurs only surprisingly close to the maximally frustrated interactions of the orbital compass model. The spin waves remain gapful at the critical point, and both the boson expansion and MERA do not find any algebraically decaying spin-spin correlations in the critical ground state.