Compass-Heisenberg model on the square lattice —Spin order and elementary excitations

Trousselet, Fabien; Oleś, Andrzej M.; Horsch, Peter

doi:10.1209/0295-5075/91/40005

Cited by 46 publications

(55 citation statements)

References 29 publications

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“…In both these cases the orbital exchange (orbital-flip) processes are blocked and orbital interaction are of a classical Ising-like form. Such Ising interactions are frustrated when they emerge in higher dimension, as in the well-studied orbital compass model [73][74][75] and in Kitaev model [76], see also a recent review on the compass model [77]. It is now intriguing to ask what happens to the SOE in this case.…”

Section: Ising Orbital Interactions (∆ = 0)mentioning

confidence: 99%

Quantum entanglement in the one-dimensional spin-orbitalSU(2)⊗XXZmodel

2015

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We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU(2)⊗XXZ model with SU(2) spin exchange and anisotropic XXZ orbital exchange interactions and negative exchange coupling. As a unique feature, the spin-orbital entanglement entropy in the entangled ground states increases here linearly with system size. In the case of Ising orbital interactions we identify an emergent phase with long-range spin-singlet dimer correlations triggered by a quadrupling of correlations in the orbital sector. The peculiar translational invariant spin-singlet dimer phase has finite von Neumann entanglement entropy and survives when orbital quantum fluctuations are included. It even persists in the isotropic SU(2)⊗SU(2) limit. Surprisingly, for finite transverse orbital coupling the long-range spin singlet correlations also coexist in the antiferromagnetic spin and alternating orbital phase making this phase also unconventional. Moreover we also find a complementary orbital singlet phase that exists in the isotropic case but does not extend to the Ising limit. The nature of entanglement appears essentially different from that found in the frequently discussed model with positive coupling. Furthermore we investigate the collective spin and orbital wave excitations of the disentangled ferromagnetic-spin/ferro-orbital ground state and explore the continuum of spin-orbital excitations. Interestingly one finds among the latter excitations two modes of exciton bound states. Their spin-orbital correlations differ from the remaining continuum states and exhibit logarithmic scaling of the von Neumann entropy with increasing system size. We demonstrate that spin-orbital excitons can be experimentally explored using resonant inelastic x-ray scattering, where the strongly entangled exciton states can be easily distinguished from the spin-orbital continuum.

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Section: Ising Orbital Interactions (∆ = 0)mentioning

confidence: 99%

Quantum entanglement in the one-dimensional spin-orbitalSU(2)⊗XXZmodel

2015

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“…It was shown by ab initio calculations that the Heisenberg superexchange is the largest low-energy scale but also Ising-like compass interactions contribute [20]. Therefore, individual Ba 2 IrO 4 layers provide a close realization of the quantum spin-1/2 compass-Heisenberg model [21]. We note that similarly complex structure of the superexchange was established for the honeycomb lattice compound Na 2 TiO 3 , where it takes the form of Kitaev-Heisenberg model which is under intense discussion at present [22].…”

Section: Introductionmentioning

confidence: 99%

Multibandd−pmodel and self-doping in the electronic structure ofBa2IrO4

Rościszewski

Oleś

2016

Phys. Rev. B

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We introduce and investigate the multiband d − p model describing a IrO4 layer (such as realized in Ba2IrO4) where all 34 orbitals per unit cell are partly occupied, i.e., t2g and eg orbitals at iridium and 2p orbitals at oxygen ions. The model takes into account anisotropic iridium-oxygen d − p and oxygen-oxygen p − p hopping processes, crystal-field splittings, spin-orbit coupling, and the on-site Coulomb interactions, both at iridium and at oxygen ions. We show that the predictions based on assumed idealized ionic configuration (with n0 = 5 + 4 × 6 = 29 electrons per IrO4 unit) do not explain well the independent ab initio data and the experimental data for Ba2IrO4. Instead we find that the total electron density in the d − p states is smaller, n = 29 − x < n0 (x > 0). When we fix x = 1, the predictions for the d − p model become more realistic and weakly insulating antiferromagnetic ground state with the moments lying within IrO2 planes along (110) direction is found, in agreement with experiment and ab initio data. We also show that: (i) holes delocalize over the oxygen orbitals and the electron density at iridium ions is enhanced, hence (ii) their eg orbitals are occupied by more than one electron and have to be included in the multiband d − p model describing iridates.

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“…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.…”

Section: Introductionmentioning

confidence: 77%

“…For example, the global ground states of the 2D QCM have a ferro-orbital nematic long-range order in a highly degenerate ground state [36,52,53]. It has been shown that this directional long-range order survives in a manifold of low energy excited states when the compass interactions are perturbed by the Heisenberg ones [37] -this property opens its potential application in quantum computation. It is remarkable that the 2D QCM is dual to the toric code model in transverse magnetic field [54] and to the Xu-Moore model (Josephson arrays) [55].…”

Section: Introductionmentioning

confidence: 99%

Quantum phase transitions in exactly solvable one-dimensional compass models

2014

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We present an exact solution for a class of one-dimensional compass models which stand for interacting orbital degrees of freedom in a Mott insulator. By employing the Jordan-Wigner transformation we map these models on noninteracting fermions and discuss how spin correlations, high degeneracy of the ground state, and Z2 symmetry in the quantum compass model are visible in the fermionic language. Considering a zigzag chain of ions with singly occupied eg orbitals (eg orbital model) we demonstrate that the orbital excitations change qualitatively with increasing transverse field, and that the excitation gap closes at the quantum phase transition to a polarized state. This phase transition disappears in the quantum compass model with maximally frustrated orbital interactions which resembles the Kitaev model. Here we find that finite transverse field destabilizes the orbital-liquid ground state with macroscopic degeneracy, and leads to peculiar behavior of the specific heat and orbital susceptibility at finite temperature. We show that the entropy and the cooling rate at finite temperature exhibit quite different behavior near the critical point for these two models.

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Compass-Heisenberg model on the square lattice —Spin order and elementary excitations

Cited by 46 publications

References 29 publications

Quantum entanglement in the one-dimensional spin-orbitalSU(2)⊗XXZmodel

Quantum entanglement in the one-dimensional spin-orbitalSU(2)⊗XXZmodel

Multibandd−pmodel and self-doping in the electronic structure ofBa2IrO4

Quantum phase transitions in exactly solvable one-dimensional compass models

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