Nonequivalence of ensembles for long-range quantum spin systems in optical lattices

Abstract

Motivated by the anisotropic long-range nature of the interactions between cold dipolar atoms or molecules in an optical lattice, we study the anisotropic quantum Heisenberg model with Curie-Weiss-type long-range interactions. Absence of a heat bath in optical lattice experiments suggests a study of this model within the microcanonical ensemble. The microcanonical entropy is calculated analytically, and nonequivalence of microcanonical and canonical ensembles is found for a range of anisotropy parameters. From the shape of the entropy it follows that the Curie-Weiss Heisenberg model is indistinguishable from the Curie-Weiss Ising model in canonical thermodynamics, although their microcanonical thermodynamics differs. Qualitatively, the observed features of nonequivalent ensembles are expected to be relevant for long-range quantum spin systems realized in optical lattice experiments.

5 pages, 1 figure

References in corpus (9)

• A High Phase-Space-Density Gas of Polar Molecules
• Bose-Einstein condensation of chromium
• A toolbox for lattice spin models with polar molecules
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Bose Condensates with 1/r Interatomic Attraction: Electromagnetically Induced ``Gravity''
• An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
• Partial equivalence of statistical ensembles and kinetic energy
• Mean-field driven first-order phase transitions in systems with long-range interactions
• Microcanonical phase diagrams of short-range ferromagnets

Cited by in corpus (41)

• Long-range interacting quantum systems
• Breakdown of quasilocality in long-range quantum lattice models
• Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
• Diverging equilibration times in long-range quantum spin models
• Dynamical critical scaling of long-range interacting quantum magnets
• Relaxation timescales and decay of correlations in a long-range interacting quantum simulator
• Pre-relaxation in weakly interacting models
• Quantum quench in long-range field theories
• Interplay of Soundcone and Supersonic Propagation in Lattice Models with Power Law Interactions
• Ensemble equivalence for general many-body systems
• One-dimensional quantum many body systems with long-range interactions
• Spreading of Perturbations in Long-Range Interacting Classical Lattice Models
• Phase transitions in systems with non-additive long-range interactions
• Many-body dynamics in long-range hopping model in the presence of correlated and uncorrelated disorder
• Spreading of Correlations and Entanglement in the Long-Range Transverse Ising Chain
• Stock returns versus trading volume: is the correspondence more general?
• Quantum chaos and ensemble inequivalence of quantum long-range Ising chains
• Supersolid stripe crystal from finite-range interactions on a lattice
• Algebraic Localization from Power-Law Interactions in Disordered Quantum Wires
• Nonequivalence of ensembles in the Curie-Weiss anisotropic quantum Heisenberg model
• Suppression of heating by long-range interactions in periodically driven spin chains
• Noise-induced dynamical phase transitions in long-range systems
• Strong ensemble nonequivalence in systems with local constraints
• Bound state dynamics in the long-range spin-$\frac{1}{2}$ XXZ model
• Effects of energy extensivity on the quantum phases of long-range interacting systems
• On the origin of power-laws in equilibrium
• Equilibrium Properties of Quantum Spin Systems with Non-additive Long-Range Interactions
• Ensemble inequivalence in long-range quantum systems
• Equilibration in long-range quantum spin systems from a BBGKY perspective
• Exact eigenspectrum of the symmetric simple exclusion process on the complete, complete bipartite, and related graphs
• Entanglement propagation and dynamics in non-additive quantum systems
• Ensemble nonequivalence and Bose-Einstein condensation in weighted networks
• Next-to-leading order perturbative contributions in the QCD sum rules for mesonic two-point correlation functions with unequal quark masses
• Subexponentially growing Hilbert space and nonconcentrating distributions in a constrained spin model
• Microcanonical analysis of the Curie-Weiss anisotropic quantum Heisenberg model in a magnetic field
• Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions
• Quantum fluctuations inhibit symmetry breaking in the HMF model
• Ensemble Inequivalence in Long-Range Quantum Spin Systems
• High-temperature partition functions and classical simulatability of long-range quantum systems
• Statistical ensembles for phase coexistence states specified by noncommutative additive observables
• Symmetries of a mean-field spin model