Geometric aspects of quantum spin states

DOI10.1007/BF02108805zbMath0799.58087arXivcond-mat/9310009MaRDI QIDQ1330936

Bruno Nachtergaele, Michael Aizenman

Publication date: 10 August 1994

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

Full work available at URL: https://arxiv.org/abs/cond-mat/9310009

zbMATH Keywords

quantum spin systems

Mathematics Subject Classification ID

Applications of global analysis to the sciences (58Z05) Statistical mechanics of ferroelectrics (82D45) Quantum equilibrium statistical mechanics (general) (82B10)

Related Items (54)

Critical parameter of random loop model on trees ⋮ Geometric aspects of quantum spin states ⋮ Improved lower bound on thermodynamic pressure of the spin 1/2 Heisenberg ferromagnet ⋮ Emptiness formation probability ⋮ The phase transition of the quantum Ising model is sharp ⋮ The free energy in a class of quantum spin systems and interchange processes ⋮ Existence of Néel order in the \(S=1\) bilinear-biquadratic Heisenberg model via random loops ⋮ Critical Parameters for Loop and Bernoulli Percolation ⋮ Critical value of the quantum Ising model on star-like graphs ⋮ On the slow decay of \(O(2)\) correlations in the absence of topological excitations: Remark on the Patrascioiu-Seiler model ⋮ Phase transition for loop representations of quantum spin systems on trees ⋮ Long-range order for the spin-1 Heisenberg model with a small antiferromagnetic interaction ⋮ Ground states for mean field models with a transverse component ⋮ Infrared bound and mean-field behaviour in the quantum Ising model ⋮ Decay of correlations in 2D quantum systems with continuous symmetry ⋮ A direct proof of dimerization in a family of \(\mathrm{SU}(n)\)-invariant quantum spin chains ⋮ Quantum spins and random loops on the complete graph ⋮ Characterising random partitions by random colouring ⋮ Heisenberg models and Schur-Weyl duality ⋮ Macroscopic loops in the Bose gas, spin \(O(N)\) and related models ⋮ Split-and-merge in stationary random stirring on lattice torus ⋮ Dimerization and Néel order in different quantum spin chains through a shared loop representation ⋮ Lattice permutations and Poisson-Dirichlet distribution of cycle lengths ⋮ Ferromagnetic ordering of energy levels for \(\mathrm{U}_q(\mathfrak{sl}_2)\) symmetric spin chains ⋮ Thermal stability of the Nagaoka-Thouless theorems ⋮ On the notion(s) of duality for Markov processes ⋮ Interplay of analysis and probability in applied mathematics. Abstracts from the workshop held February 11--17, 2018 ⋮ Dimerization in quantum spin chains with \(O(n)\) symmetry ⋮ PATH INTEGRAL REPRESENTATION FOR INTERFACE STATES OF THE ANISOTROPIC HEISENBERG MODEL ⋮ Critical region for an Ising model coupled to causal triangulations ⋮ On a model of random cycles ⋮ Random loop representations for quantum spin systems ⋮ A multi-dimensional Lieb-Schultz-Mattis theorem ⋮ Thermodynamics and universality for mean field quantum spin glasses ⋮ The phase diagram of the quantum Curie-Weiss model ⋮ Critical temperature of Heisenberg models on regular trees, via random loops ⋮ Fermionic observables in the transverse Ising chain ⋮ Lieb-Schultz-Mattis type theorems for quantum spin chains without continuous symmetry ⋮ On gapped phases with a continuous symmetry and boundary operators ⋮ Random current representation for transverse field Ising model ⋮ The interchange process with reversals on the complete graph ⋮ General Lieb-Schultz-Mattis type theorems for quantum spin chains ⋮ Vertex models and random labyrinths: phase diagrams for ice-type vertex models ⋮ Bounded entanglement entropy in the quantum Ising model ⋮ Field theory of compact polymers on the square lattice ⋮ Intersecting loop models on \({\mathbb Z}^ d\): rigorous results. ⋮ Sharp phase transition for random loop models on trees ⋮ Critical point for infinite cycles in a random loop model on trees ⋮ Decay of transverse correlations in quantum Heisenberg models ⋮ Low-temperature phase diagrams of quantum lattice systems. I: Stability for quantum perturbations of classical systems with finitely-many ground states. ⋮ Gibbs measures on permutations over one-dimensional discrete point sets ⋮ Vanishing critical magnetization in the quantum Ising model ⋮ Translation invariant pure state on B=⊗j∈ZMd(j)(C) and its split property ⋮ Fermionic and bosonic Laughlin state on thick cylinders

Cites Work

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