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

TL;DR

This paper demonstrates that quasilocal conserved charges are essential for accurately describing stationary states in integrable quantum field theories with non-diagonal scattering, extending the concept from lattice models to continuum theories like sine-Gordon.

Contribution

It identifies the necessity of quasilocal charges in the GGE for non-diagonal scattering theories and explicitly constructs these charges for the sine-Gordon model.

Findings

Quasilocal charges are necessary for the GGE in non-diagonal scattering theories.

The set of charges in the sine-Gordon model includes fractional spin local charges.

Lattice quasilocal charges become local charges with fractional spin in the continuum limit.

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.