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

Quantum phase transitions in exactly solvable one-dimensional compass models

“…In the latter case the operators include just one of the orthogonal pseudospin components at each bond and are Ising-like. This form of interactions is found as well in the compass models [28][29][30][31][32][33][34][35][36][37][38][39], and in the Kitaev model on the honeycomb lattice [40][41][42]. The interactions that are considered here are defined by the pseudospin operators T γ i for two active orbitals (for T = 1/2), and we define them as linear combinations of the Pauli matrices {σ These operators define the generalized compass model (GCM) considered in this paper.…”

“…This frustration increases gradually with increasing angle θ when the model Eq. (1.3) interpolates between the Ising model at θ = 0 to the quantum compass model (QCM) at θ = π/2 [35]. The latter is also called the 1D Kitaev model by some authors [42].…”

“…(1.3) with frustrated Ising-like interactions tuned by an angle θ on a square lattice [35] at θ = 90…”

Quantum phase transitions in a generalized compass chain with three-site interactions

“…With increasing angle θ, frustration gradually increases when the model Eq. (1) interpolates between the Ising model at θ = 0 and the quantum compass model (QCM) at θ = π/2, in analogy to the 2D compass model [47]. The model was solved exactly and the ground state is found to have order along the easy axis as long as θ = π/2, whereas it becomes a highly disordered spinliquid ground state at θ = π/2 [48,49].…”

Exotic Spin Order due to Orbital Fluctuations

“…Frustrated spin models are known to exhibit very interesting properties and have frequently exotic ground states [26]. In systems with active orbital degrees of freedom such states may arise from intrinsic frustration of orbital interactions which, unlike the spin ones with SU(2) symmetry, are directional both in the e g orbital models [27][28][29] and in the compass model [30][31][32][33][34] -they contain terms which compete with one another. Studies of such models require more sophisticated approaches than the singlesite mean field (MF) approximation or linear spin-wave expansion.…”