Compass-Heisenberg Model on the Square Lattice : Spin Order and Excitations

Abstract

We explore the physics of the anisotropic compass model under the influence of perturbing Heisenberg interactions and present the phase diagram with multiple quantum phase transitions. The macroscopic ground state degeneracy of the compass model is lifted in the thermodynamic limit already by infinitesimal Heisenberg coupling, which selects different ground states with Z_2 symmetry depending on the sign and size of the coupling constants --- then low energy excitations are spin waves, while the compass states reflecting columnar order are separated from them by a macroscopic gap. Nevertheless, nanoscale structures relevant for quantum computation purposes may be tuned such that the compass states are the lowest energy excitations, thereby avoiding decoherence, if a size criterion derived by us is fulfilled.

6 pages, 5 figures

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• Multicriticality and entanglement in the one-dimensional quantum compass model
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Cited by in corpus (36)

• Fingerprints of spin-orbital entanglement in transition metal oxides
• Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature
• Spin-orbital physics for p orbitals in alkali RO_2 hyperoxides --- generalization of the Goodenough-Kanamori rules
• Spin-orbital resonating valence bond liquid on a triangular lattice: Evidence from finite-cluster diagonalization
• Magnetic properties of nanoscale compass-Heisenberg planar clusters
• Entangled spin-orbital phases in the bilayer Kugel-Khomskii model
• Quantum phase transitions in exactly solvable one-dimensional compass models
• Hidden Quasiparticles and Incoherent Photoemission Spectra in Na2IrO3
• Quantum Many-Body Scars in Spin-1 Kitaev Chains
• Topological Order in an Entangled SU(2)$\otimes$XY Spin-Orbital Ring
• Quantum coherence in a compass chain under an alternating magnetic field
• Symmetry properties and spectra of the two-dimensional quantum compass model
• Overcoming the Sign Problem at Finite Temperature: Quantum Tensor Network for the Orbital $e_g$ Model on an Infinite Square Lattice
• Macroscopic Degeneracy and Emergent Frustration in a Honeycomb Lattice Magnet
• Anisotropic magnetic interactions in hexagonal AB-stacked kagome lattice structures: Applications to ${\mathrm{Mn}}_3\mathrm{X}$ ($\mathrm{X}$ = $\mathrm{Ge}$, $\mathrm{Sn}$, $\mathrm{Ga}$) compounds
• Pseudo-Goldstone modes and dynamical gap generation from order-by-thermal-disorder
• Emergent dimensional reduction of the spin sector in a model for narrow-band manganites
• Quantum phase transitions in the spin-1 Kitaev-Heisenberg chain
• Quantum entanglement in the one-dimensional spin-orbital SU(2)$\otimes XXZ$ model
• Frustration and Entanglement in Compass and Spin-Orbital Models
• Valence Bond Crystal and possible orbital pinball liquid in a t2g model
• Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice
• Mechanism of hole propagation in the orbital compass models
• Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy
• Spin-Orbital Entanglement Emerging from Frustration in the Kugel-Khomskii Model
• Locally tunable disorder and entanglement in the one-dimensional plaquette orbital model
• Magnetic order and spin excitations in layered Heisenberg antiferromagnets with compass-model anisotropies
• Multiband $d-p$ model and self-doping in the electronic structure of Ba${}_2$IrO${}_4$
• Ground state properties of the Heisenberg-compass model on the square lattice
• Striped critical spin liquid in a spin-orbital entangled RVB state in a projected entangled-pair state representation
• Hole propagation in the orbital compass models
• Exact Ground States and Phase Diagram of the Quantum Compass Model under an in-plane Field
• Exotic Spin Order due to Orbital Fluctuations
• One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization
• Quantum phase transitions in the Kitaev--Heisenberg model on a single hexagon
• Phase diagram and Ashkin-Teller universality in the classical square-lattice Heisenberg-compass model