Quasilocal charges and progress towards the complete GGE for field theories with non-diagonal scattering

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-$\frac{1}{2}$ XXZ Heisenberg chain. These charges have been proven to be essential for properly describing 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 non-diagonal scattering. A stationary state in a non-diagonal scattering theory is completely specified by fixing the mode-ocuppation 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, are unable to fix the distributions of these auxiliary particles, since these charges can only fix kinematical properties of physical particles. The field theory analogs of 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 are shown to become a set local charges with fractional spin in the field theory.

v1: 30 pages, 4 figures v2: 35 pages, 5 figures; reorganization of the manuscript's structure, some discussions and references added

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Cited by in corpus (12)

• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics
• Entanglement spreading in non-equilibrium integrable systems
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Exact solution for the quench dynamics of a nested integrable system
• Exact Thermodynamics and Transport in the Classical Sine-Gordon Model
• Diffusive Hydrodynamics of Inhomogenous Hamiltonians
• Quantum quench in the attractive regime of the sine-Gordon model
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
• The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
• Popcorn Drude weights from quantum symmetry
• Anomalous charge transport in the sine-Gordon model