Frustration and Entanglement in Compass and Spin-Orbital Models

Abstract

We review the consequences of intrinsic frustration of the orbital superexchange and of spin-orbital entanglement. While Heisenberg perturbing interactions remove frustration in the compass model, the lowest columnar excitations are robust in the nanoscopic compass clusters and might be used for quantum computations. Entangled spin-orbital states determine the ground states in some cases, while in others concern excited states and lead to measurable consequences, as in the $R$VO${}_3$ perovskites. On-site entanglement for strong spin-orbit coupling generates the frustrated Kitaev-Heisenberg model with a rich magnetic phase diagram on the honeycomb lattice. Frustration is here reflected in hole propagation which changes from coherent in an antiferromagnet via hidden quasiparticles in zigzag and stripe phases to entirely incoherent one in the Kitaev spin liquid.

arXiv comment8 pages, 5 figures, invited talk at PM'14 Conference, Poznan, June 2014

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Cited by in corpus (15)

• Frustration and quantum criticality
• Antiferromagnetic Kitaev Interaction in $f$-Electron Based Honeycomb Magnets
• Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature
• Quantum phase transitions in a generalized compass chain with three-site interactions
• Overcoming the Sign Problem at Finite Temperature: Quantum Tensor Network for the Orbital $e_g$ Model on an Infinite Square Lattice
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• Quantum entanglement in the one-dimensional spin-orbital SU(2)$\otimes XXZ$ model
• Green's function variational approach to orbital polarons in KCuF3
• Spin-orbital model of stoichiometric LaMnO${}_3$ with tetragonal distortions
• Charge transfer model for the electronic structure of layered ruthenates
• Magnon dressing by orbital excitations in ferromagnetic planes of K${}_2$CuF${}_4$ and LaMnO${}_3$
• Hole propagation in the orbital compass models
• One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization
• Quantum phase transitions in the Kitaev--Heisenberg model on a single hexagon
• Order in Quantum Compass and Orbital $e_g$ Models