Compass-Heisenberg Model on the Square Lattice : Spin Order and Excitations

TL;DR

This paper investigates how Heisenberg interactions influence the phase diagram and ground state degeneracy of the anisotropic compass model on a square lattice, with implications for quantum computation.

Contribution

It presents a detailed phase diagram showing quantum phase transitions and analyzes how infinitesimal Heisenberg coupling lifts ground state degeneracy in the compass model.

Findings

Heisenberg coupling lifts ground state degeneracy in the thermodynamic limit.

Low energy excitations are spin waves separated by a macroscopic gap from compass states.

Nanoscale structures can be tuned to maintain compass states as lowest energy excitations.

Abstract

We explore the physics of the anisotropic compass model under the influence of perturbing Heisenberg interactions and present the phase diagram with multiple quantum phase transitions. The macroscopic ground state degeneracy of the compass model is lifted in the thermodynamic limit already by infinitesimal Heisenberg coupling, which selects different ground states with Z_2 symmetry depending on the sign and size of the coupling constants --- then low energy excitations are spin waves, while the compass states reflecting columnar order are separated from them by a macroscopic gap. Nevertheless, nanoscale structures relevant for quantum computation purposes may be tuned such that the compass states are the lowest energy excitations, thereby avoiding decoherence, if a size criterion derived by us is fulfilled.