In the present paper, we study the properties of the two-dimensional quantum compass model by a mathematically rigorous approach. Based on the Perron?Fr?benius theorem and the reflection positivity method, we show that the low-energy spectrum of this model is of one-dimensional type. Furthermore, its global ground states have a directional long-range order. Our results confirm several previous conclusions obtained by either numerical or perturbation calculations

Journal of Physics A Mathematical and TheoreticalJun 11, 201015 citations

Solid State Communications

Effects of Heisenberg perturbation on the ground-state properties of one-dimensional extended quantum compass model

Guanghua Liu, Longjuan Kong, Xiaoyan Deng, Wen‐Long You

Published Mar 5, 2015• 1 citation

Publisher

DOI: 10.1016/j.ssc.2015.02.022

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We study a model of spins

1/2

on a square lattice, generalizing the quantum compass model via the addition of perturbing Heisenberg interactions between nearest neighbors, and investigate its phase diagram and magnetic excitations. This model has motivations both from the field of strongly correlated systems with orbital degeneracy and from that of solid-state based devices proposed for quantum computing. We find that the high degeneracy of ground states of the compass model is fragile and changes into twofold degenerate ground states for any finite amplitude of Heisenberg coupling. By computing the spin structure factors of finite clusters with L\'anczos diagonalization, we evidence a rich variety of phases characterized by

{\mathbb{Z}}_{2}

symmetry that are either ferromagnetic,

C

-type antiferromagnetic, or of the N\'eel type and analyze the effects of quantum fluctuations on phase boundaries. In the ordered phases, the anisotropy of compass interactions leads to a finite excitation gap to spin waves. We show that for small nanoscale clusters with large anisotropy gap the lowest excitations are column-flip excitations that emerge due to Heisenberg perturbing interactions from the manifold of degenerate ground states of the compass model. We derive an effective one-dimensional

XYZ

model that faithfully reproduces the exact structure of these excited states and elucidates their microscopic origin. The low-energy column-flip or compass-type excitations are robust against decoherence processes and are therefore well designed for storing information in quantum computing. We also point out that the dipolar interactions between nitrogen-vacancy centers forming a rectangular lattice in a diamond matrix may permit a solid-state realization of the anisotropic compass-Heisenberg model.