FREE ENERGY DENSITY FOR MEAN FIELD PERTURBATION OF STATES OF A ONE-DIMENSIONAL SPIN CHAIN

DOI10.1142/S0129055X08003298zbMath1153.82002arXiv0706.4148OpenAlexW3101879820MaRDI QIDQ3532412

Fumio Hiai, Hiromichi Ohno, Milán Mosonyi, Dénes Petz

Publication date: 3 November 2008

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.4148

zbMATH Keywords

KMS statesGibbs statesLegendre transformationfree energy densityKubo-Martin-Schwinger statesquantum Markov statescorrelated statesmean relative entropy

Mathematics Subject Classification ID

Quantum equilibrium statistical mechanics (general) (82B10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (7)

Classical dynamics generated by long-range interactions for lattice fermions and quantum spins ⋮ Translation invariant pure state on \(\bigotimes _{\mathbb {Z}}M_d(\mathbb C)\) and Haag duality ⋮ RUELLE–LANFORD FUNCTIONS AND LARGE DEVIATIONS FOR ASYMPTOTICALLY DECOUPLED QUANTUM SYSTEMS ⋮ EFFECT OF A LOCALLY REPULSIVE INTERACTION ON s-WAVE SUPERCONDUCTORS ⋮ A NOTE ON THE NON-COMMUTATIVE LAPLACE–VARADHAN INTEGRAL LEMMA ⋮ Large deviations in quantum spin chains ⋮ Non–cooperative equilibria of Fermi systems with long range interactions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Structure of sufficient quantum coarse-grainings
• On general minimax theorems
• Large deviations for quantum spin systems
• Equivalent forms of the Bessis-Moussa-Villani conjecture
• Elementary proof for Sion's minimax theorem
• The proper formula for relative entropy and its asymptotics in quantum probability
• Finitely correlated states on quantum spin chains
• The Golden-Thompson trace inequality is complemented
• On uniqueness of KmMS states of one-dimensional quantum lattice systems
• On uniqueness of KMS states of one-dimensional quantum lattice systems
• Entropy densities for algebraic states
• Non-homogeneous quantum Markov states and quantum Markov fields
• Asymptotic of Varadhan-type and the Gibbs variational principle
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Gibbs states of a one dimensional quantum lattice
• Conditional expectations in von Neumann algebras
• Large deviations in quantum lattice systems: one-phase region
• Monotonic converging variational approximations to the functional integrals in quantum statistical mechanics
• QUANTUM MARKOV FIELDS
• Large deviations and Chernoff bound for certain correlated states on a spin chain
• ENTROPY DENSITIES FOR GIBBS STATES OF QUANTUM SPIN SYSTEMS
• Equality cases in matrix norm inequalities of golden-thompson type
• MARKOVIAN KMS-STATES FOR ONE-DIMENSIONAL SPIN CHAINS

This page was built for publication: FREE ENERGY DENSITY FOR MEAN FIELD PERTURBATION OF STATES OF A ONE-DIMENSIONAL SPIN CHAIN