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arXiv:2310.01384 · Physical review. B./Physical review. B

Exact ground states and phase diagram of the quantum compass model under an in-plane field

A. D. S. Richards, Erik Schwartz Sørensen

Published Jun 26, 2024• 3 citations
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Abstract

We consider the square lattice $S=1/2$ quantum compass model (QCM) parametrized by ${J}_{x},{J}_{z}$, under a field, $\mathbf{h}$, in the $x\text{\ensuremath{-}}z$ plane. At the special field value $({h}_{x}^{★},{h}_{z}^{★})=2S({J}_{x},{J}_{z})$, we show that the QCM Hamiltonian may be written in a form such that two simple product states can be identified as exact ground states, below a gap. Exact excited states can also be found. We use the staggered vector chirality to characterize the exact ground states at $({h}_{x}^{★},{h}_{z}^{★})$ and states obtained for fields within the vicinity of $({h}_{x}^{★},{h}_{z}^{★})$. This gapped phase occupies most of the in-plane field phase diagram. For some values of ${h}_{x}>{h}_{z}$ and ${h}_{z}>{h}_{x}$ at the edges of the phase diagram, we have found transitions between this gapped phase and phases of weakly coupled Ising-chain states. In zero field, the QCM is known to have an emergent subextensive ground-state degeneracy. As the field is increased from zero, we find that this degeneracy is partially lifted, resulting in bond-oriented spin-stripe states, which are each separated from one another and the gapped phase by first-order transitions. Our findings are important for understanding the field dependent phase diagram of materials with predominantly directionally dependent Ising interactions.

DOI
10.1103/physrevb.109.l241116

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We study a model of spins 1/21/21/2 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 Z2{\mathbb{Z}}_{2}Z2​ symmetry that are either ferromagnetic, CCC-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 XYZXYZXYZ 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.
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The quantum compass model consists of a two-dimensional square spin lattice where the orientation of the spin–spin interactions depends on the spatial direction of the bonds. It has remarkable symmetry properties and the ground state shows topological degeneracy. The implementation of the quantum compass model in quantum simulation setups like ultracold atoms and trapped ions is far from trivial, since spin interactions in those systems typically are independent of the spatial direction. Ising spin interactions, on the contrary, can be induced and controlled in atomic setups with state-of-the art experimental techniques. In this work, we show how the quantum compass model on a rectangular lattice can be simulated by the use of the photon-assisted tunneling induced by periodic drivings on a quantum Ising spin model. We describe a procedure to adiabatically prepare one of the doubly degenerate ground states of this model by adiabatically ramping down a transverse magnetic field, with surprising differences depending on the parity of the lattice size. Exact diagonalizations confirm the validity of this approach for small lattices. Specific implementations of this scheme are presented with ultracold atoms in optical lattices in the Mott insulator regime, as well as with Rydberg atoms.