667 research outputs found
Stationary points approach to thermodynamic phase transitions
Nonanalyticities of thermodynamic functions are studied by adopting an
approach based on stationary points of the potential energy. For finite
systems, each stationary point is found to cause a nonanalyticity in the
microcanonical entropy, and the functional form of this nonanalytic term is
derived explicitly. With increasing system size, the order of the nonanalytic
term grows, leading to an increasing differentiability of the entropy. It is
found that only "asymptotically flat" stationary points may cause a
nonanalyticity that survives in the thermodynamic limit, and this property is
used to derive an analytic criterion establishing the existence or absence of
phase transitions. We sketch how this result can be employed to analytically
compute transition energies of classical spin models.Comment: 5 pages, 2 figures. Contribution to the proceedings of the 11th
Granada Seminar on Computational Physic
Nonequivalence of ensembles for long-range quantum spin systems in optical lattices
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.Comment: 5 pages, 1 figur
Entanglement-enhanced spreading of correlations
Starting from a product initial state, equal-time correlations in
nonrelativistic quantum lattice models propagate within a lightcone-like causal
region. The presence of entanglement in the initial state can modify this
behavior, enhancing and accelerating the growth of correlations. In this paper
we give a quantitative description, in the form of Lieb-Robinson-type bounds on
equal-time correlation functions, of the interplay of dynamics vs. initial
entanglement in quantum lattice models out of equilibrium. We test the bounds
against model calculations, and also discuss applications to quantum quenches,
quantum channels, and Kondo physics.Comment: 15 pages, 4 figure
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