Quantum spin systems on infinite lattices. A concise introduction

DOI10.1007/978-3-319-51458-1zbMath1375.82002arXiv1311.2717OpenAlexW1792932672MaRDI QIDQ528890

Pieter Naaijkens

Publication date: 17 May 2017

Published in: Lecture Notes in Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.2717

zbMATH Keywords

operator algebrasbraidingground statesKMS statesGibbs stateslocal quantum physicsLieb-Robinson boundsscattering statesquantum many-body physicscorrelations of local observablesexistence of the dynamicsexponential clustering theoremfinite and infinite lattice systemsgapped phasesGelfand-Najmark-Segal (GNS) constructioninequivalence of representationsKitaev model (toric code)Lieb-Robinson velocitypropagation of correlations in quantum lattice systemsstates space of a \(C^*\)-algebrassuperselection criterionsuperselection theorythermodynamics limit

Mathematics Subject Classification ID

Quantum field theory on lattices (81T25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) General theory of (C^*)-algebras (46L05) Many-body theory; quantum Hall effect (81V70) Quantum equilibrium statistical mechanics (general) (82B10) Operator algebra methods applied to problems in quantum theory (81R15) States of selfadjoint operator algebras (46L30) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics (82-01) Quantum coherence, entanglement, quantum correlations (81P40) Quantum coding (general) (81P70)

Related Items (10)

Continuous dependence on the initial data in the Kadison transitivity theorem and GNS construction ⋮ An entropic invariant for 2D gapped quantum phases ⋮ Generalized phase-space techniques to explore quantum phase transitions in critical quantum spin systems ⋮ The Wasserstein distance of order 1 for quantum spin systems on infinite lattices ⋮ Almost everywhere ergodicity in quantum lattice models ⋮ Long-time dynamics in quantum spin lattices: ergodicity and hydrodynamic projections at all frequencies and wavelengths ⋮ The adiabatic theorem in a quantum many-body setting ⋮ Fusion rules from entanglement ⋮ Hydrodynamic projections and the emergence of linearised Euler equations in one-dimensional isolated systems ⋮ Quasi-locality bounds for quantum lattice systems. II: perturbations of frustration-free spin models with gapped ground states

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