Spontaneous symmetry breaking in a generalized orbital compass model

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.

9 pages, 6 figures, improved presentation, version to appear in Phys. Rev. B

References in corpus (18)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• A class of quantum many-body states that can be efficiently simulated
• New Trends in Density Matrix Renormalization
• Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice
• Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
• Unitary circuits for strongly correlated fermions
• Quantum MERA Channels
• First order phase transition in the anisotropic quantum orbital compass model
• Orbital order in classical models of transition-metal compounds
• Evolution of Spin-Orbital-Lattice Coupling in the $R$VO${}_3$ Perovskites
• Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
• Unifying variational methods for simulating quantum many-body systems
• Multicriticality and entanglement in the one-dimensional quantum compass model
• Microscopic modelling of doped manganites
• Topologically decoherence-protected qubits with trapped ions
• Spin--orbital physics in transition metal oxides
• Entanglement renormalization and boundary critical phenomena
• Orbital fluctuations in the $R$VO${}_3$ perovskites

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