Subexponentially growing Hilbert space and nonconcentrating distributions in a constrained spin model
arXiv:1706.09832 · doi:10.1007/s10955-018-2016-y
Abstract
Motivated by recent experiments with two-component Bose-Einstein condensates, we study fully-connected spin models subject to an additional constraint. The constraint is responsible for the Hilbert space dimension to scale only linearly with the system size. We discuss the unconventional statistical physical and thermodynamic properties of such a system, in particular the absence of concentration of the underlying probability distributions. As a consequence, expectation values are less suitable to characterize such systems, and full distribution functions are required instead. Sharp signatures of phase transitions do not occur in such a setting, but transitions from singly peaked to doubly peaked distribution functions of an "order parameter" may be present.
15 pages, 6 figures
References in corpus (20)
- The large deviation approach to statistical mechanics
- Nonlinear atom interferometer surpasses classical precision limit
- Quantum Superposition States of Bose-Einstein Condensates
- Fisher Information and entanglement of non-Gaussian spin states
- Classical bifurcation at the transition from Rabi to Josephson dynamics
- Measuring multipartite entanglement via dynamic susceptibilities
- Signatures of Many-Body Localization in a Controlled Open Quantum System
- Excited state quantum phase transitions in many-body systems
- The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
- Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model
- Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
- Entanglement Entropy beyond the Free Case
- Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation
- Nonequivalence of ensembles for long-range quantum spin systems in optical lattices
- Degenerate Bose-Fermi mixtures of rubidium and ytterbium
- Spin squeezing by tensor twisting and Lipkin-Meshkov-Glick dynamics in a toroidal Bose-Einstein condensate with spatially modulated nonlinearity
- Nonequivalence of ensembles in the Curie-Weiss anisotropic quantum Heisenberg model
- Finite-Temperature Fidelity-Metric Approach to the Lipkin-Meshkov-Glick Model
- Finite Temperature Many-Body Theory with the Lipkin Model
- Microcanonical analysis of the Curie-Weiss anisotropic quantum Heisenberg model in a magnetic field