From interacting particles to equilibrium statistical ensembles

Abstract

We argue that a particle language provides a conceptually simple framework for the description of anomalous equilibration in isolated quantum systems. We address this paradigm in the context of integrable models, which are those with particles that are stable against decay. In particular, we demonstrate that a complete description of equilibrium ensembles for interacting integrable models requires a formulation built from the mode occupation numbers of the underlying particle content, mirroring the case of non-interacting particles. This yields an intuitive physical interpretation of generalized Gibbs ensembles, and reconciles them with the microcanonical ensemble. We explain how previous attempts to identify an appropriate ensemble overlooked an essential piece of information, and provide explicit examples in the context of quantum quenches.

Current operators in integrable spin chains: lessons from long range deformations

“…Typically the amplitudes decay exponentially with the range. The quasi-local operators play an essential role in the description of the Generalized Gibbs Ensemble of Heisenberg spin chain and related models [17,18,19,20,21,22]. There a commuting set of quasi-local charges is derived from the fused transfer matrices.…”

Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz

“…This is the ultimate form of the GETH, relevant for interacting integrable models. This idea was further formalized in [51,52], where it was argued that the GGE should be formulated using root density operators, whose eigenvalues are the root densities themselves.…”

“…It follows that this set of charges is not sufficient to determine all Bethe root densities: X 1 (u) only fixes the hole density of the 1-strings. This situation was remedied in [24] (see also [47,51]), where it was shown that the recently introduced quasi-local charges [25,26] contain just enough information to fix all the root densities.…”

Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem

“…One of the simplest example is that of a homogeneous system where time evolution after a quantum quench is expected to lead to relaxation to thermal equilibrium. However, in the case of integrable system thermalisation is absent and the steady state was proposed to be described by the generalised Gibbs ensemble (GGE) [13] which is supported by experimental and theoretical studies [4,[14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Nevertheless, important issues such as a theoretical description of the eventual time evolution, as well as the complete set of relevant conserved quantities necessary for the construction of the steady state ensemble are still open in general.…”