2016/09/30 by Eric Vernier, Axel Cortés Cubero · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Charge (physics) #Field (mathematics) #Field theory (psychology) #Integrable system #Lattice (music) #Physics of Superconductivity and Magnetism #Quantum #Quantum field theory #Quantum many-body systems #Spin (aerodynamics) #Stationary state #cond-mat.stat-mech #cond-mat.str-el #hep-lat #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1742-5468/aa5288
published as Journal of Statistical Mechanics: Theory and Experiment 2017 (2), 023101 · v1: 30 pages, 4 figures v2: 35 pages, 5 figures; reorganization of the manuscript's structure, some discussions and references added
arxiv created 2016/12/10 · openalex publication_date 2017/01/31 · openalex created_date 2017/02/10 · arxiv updated 2017/03/21 · openalex updated_date 2026/08/05
Abstract It has recently been shown that some integrable spin chains possess a set of quasilocal conserved charges, with the classic example being the spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mstyle> </mml:math> XXZ Heisenberg chain. These charges have been proven to be essential in order to properly describe stationary states after a quantum quench, and must be included in the generalized Gibbs ensemble (GGE). We find that similar charges are also necessary for the GGE description of integrable quantum field theories with nondiagonal scattering. A stationary state in a nondiagonal scattering theory is completely specified by fixing the mode-occupation density distributions of physical particles, as well auxiliary particles which carry no energy or momentum. We show that the set of conserved charges with integer Lorentz spin, related to the integrability of the model, is unable to fix the distributions of these auxiliary particles, since these charges can only fix the kinematical properties of physical particles. The field theory analogs of the quasilocal lattice charges are therefore necessary. As a concrete example, we find the complete set of charges needed in the sine-Gordon model, by using the fact that this field theory is recovered as the continuum limit of a spatially inhomogeneous version of the XXZ chain. The set of quasilocal charges of the lattice theory is shown to become a set of local charges with fractional spin in the field theory.