Pseudo-Goldstone modes and dynamical gap generation from order-by-thermal-disorder

Abstract

Accidental ground state degeneracies -- those not a consequence of global symmetries of the Hamiltonian -- are inevitably lifted by fluctuations, often leading to long-range order, a phenomenon known as "order-by-disorder" (ObD). The detection and characterization of ObD in real materials currently lacks clear, qualitative signatures that distinguish ObD from conventional energetic selection. We show that for order-by-thermal-disorder (ObTD) such a signature exists: a characteristic temperature dependence of the fluctuation-induced pseudo-Goldstone gap. We demonstrate this in a minimal two-dimensional model that exhibits ObTD, the ferromagnetic Heisenberg-compass model on a square lattice. Using spin-dynamics simulations and self-consistent mean-field calculations, we determine the pseudo-Goldstone gap, $\Delta$, and show that at low temperatures it scales as the square root of temperature, $\sqrt{T}$. We establish that a power-law temperature dependence of the gap is a general consequence of ObTD, showing that all key features of this physics can be captured in a simple model of a particle moving in an effective potential generated by the fluctuation-induced free energy.

Main text: 7 pages and 3 figures. Supplemental material: 8 pages and 3 figures

References in corpus (14)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Spontaneous Magnon Decays
• Geometric Frustration in Buckled Colloidal Monolayers
• Experimental identification of quantum spin liquids
• Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• Robustness of basal-plane antiferromagnetic order and the $J_{eff}=1/2$ state in single-layer iridate spin-orbit Mott insulators
• Magnetic field effect on topological spin excitations in CrI${}_3$
• Energetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet
• Order by Disorder and Energetic Selection of the Ground State in the XY Pyrochlore Antiferromagnet Er2Ti2O7. An Inelastic Neutron Scattering Study
• Order-by-disorder in the antiferromagnetic Ising model on an elastic triangular lattice
• Thermal Evolution of Dirac Magnons in the Honeycomb Ferromagnet CrBr${}_3$
• Quasi-Nambu-Goldstone modes in nonrelativistic systems
• Compass Impurity Model of Tb Substitution in Sr2IrO4

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• Exact Ground States and Phase Diagram of the Quantum Compass Model under an in-plane Field
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• Constructing Emergent U(1) Symmetries in the Gamma-prime $\left({\mathbf{\Gamma }}^{\prime }\right)$ model
• Anharmonic Collective Oscillations in Isotropic Spin Systems and their Spectroscopic Signatures
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• Phase diagram and Ashkin-Teller universality in the classical square-lattice Heisenberg-compass model