Directional Ordering of Fluctuations in a Two-dimensional Compass Model

Abstract

In the Mott insulating phase of the transition metal oxides, the effective orbital-orbital interaction is directional both in the orbital space and in the real space. We discuss a classical realization of directional coupling in two dimensions. Despite extensive degeneracy of the ground state, the model exhibits partial orbital ordering in the form of directional ordering of fluctuations at low temperatures stabilized by an entropy gap. Transition to the disordered phase is shown to be in the Ising universality class through exact mapping and multicanonical Monte Carlo simulations.

4 pages, revtex, 2 figures

References in corpus (9)

• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• Orbital liquid in three dimensional Mott insulator: $LaTi{O}_3$
• Spin Dynamics and Orbital State in LaTiO_3
• Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus
• Orbital ordering and frustrations
• Order from disorder: Quantum spin gap in magnon spectra of LaTiO_3
• Orbital order in classical models of transition-metal compounds
• Orbitally Degenerate Spin-1 Model for Insulating V2O3
• Orbital ordering in charge transfer insulators

Cited by in corpus (50)

• A symmetry principle for Topological Quantum Order
• The Quantum Compass Model on the Square Lattice
• Generalized Elitzur's Theorem and Dimensional Reduction
• Discrete Sliding Symmetries, Dualities, and Self-dualities of Quantum Orbital Compass Models and (p+ip) Superconducting Arrays
• First order phase transition in the anisotropic quantum orbital compass model
• Z_2-vortex lattice in the ground state of the triangular Kitaev-Heisenberg model
• Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
• Nature of the Quantum Phase Transition in Quantum Compass Model
• Interacting Majorana Fermions
• Compass-Heisenberg Model on the Square Lattice : Spin Order and Excitations
• Mechanism of basal-plane antiferromagnetism in the spin-orbit driven iridate Ba2IrO4
• Spontaneous symmetry breaking in a generalized orbital compass model
• Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions
• Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature
• Fidelity susceptibility in the two-dimensional spin-orbit models
• Doubly degenerate orbital system in honeycomb lattice: implication of orbital state in layered iron oxide
• Dilution Effects in Two-dimensional Quantum Orbital System
• Quantum phase transition in the one-dimensional period-two and uniform compass model
• Quantum phase transitions in exactly solvable one-dimensional compass models
• Macroscopic Degeneracy and Emergent Frustration in a Honeycomb Lattice Magnet
• Orbital order driven quantum criticality
• Quantum spin systems at positive temperature
• Intermediate Symmetries In Electronic Systems: Dimensional Reduction, Order Out Of Disorder, Dualities, And Fractionalization
• Emergent dimensional reduction of the spin sector in a model for narrow-band manganites
• The Quantum Compass Model on the Square and Simple Cubic Lattices
• Unveiling the nature of three dimensional orbital ordering transitions: the case of $e_g$ and $t_{2g}$ models on the cubic lattice
• The quantum compass chain in a transverse magnetic field
• The emergence of Resonating Valence Bond physics in spin-orbital models
• Compass and Kitaev models -- Theory and Physical Motivations
• Mechanism of hole propagation in the orbital compass models
• Finite-Temperature Néel Ordering of Fluctuations in a Plaquette Orbital Model
• Majorana stripe order on the surface of a three-dimensional topological insulator
• From fidelity to entanglement of entropy of the one-dimensional transverse-field quantum compass model
• Thermal Canting of Spin-Bond Order
• First-order directional ordering transition in the three-dimensional compass model
• A simple framework for contrastive learning phases of matter
• Monte Carlo study of the critical properties of the three-dimensional 120-degree model
• Orbital Compass Model as an Itinerant Electron System
• Robust Topological Degeneracy of Classical Theories
• True nature of long-range order in a plaquette orbital model
• Ground state properties of the Heisenberg-compass model on the square lattice
• Interacting Majorana modes at surfaces of noncentrosymmetric superconductors
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• Hybrid Local-Order Mechanism for Inversion Symmetry Breaking
• Exact Ground States and Phase Diagram of the Quantum Compass Model under an in-plane Field
• Nonthermal order by disorder
• Hybrid Symmetry Breaking in Classical Spin Models With Subsystem Symmetries
• Phase diagram of a square lattice model of XY Spins with direction-dependent interactions
• Subsystem symmetries, critical Bose surface, and immobile excitations in an extended compass model
• Phase diagram and Ashkin-Teller universality in the classical square-lattice Heisenberg-compass model