Abstract
Generalized Hydrodynamics is a recent theory that describes large scale transport properties of one dimensional integrable models. It is built on the (typically infinitely many) local conservation laws present in these systems, and leads to a generalized Euler type hydrodynamic equation. Despite the successes of the theory, one of its cornerstones, namely a conjectured expression for the currents of the conserved charges in local equilibrium has not yet been proven for interacting lattice models. Here we fill this gap, and compute an exact result for the mean values of current operators in Bethe Ansatz solvable systems, valid in arbitrary finite volume. Our exact formula has a simple semi-classical interpretation: the currents can be computed by summing over the charge eigenvalues carried by the individual bare particles, multiplied with an effective velocity describing their propagation in the presence of the other particles. Remarkably, the semi-classical formula remains exact in the interacting quantum theory, for any finite number of particles and also in the thermodynamic limit. Our proof is built on a form factor expansion and it is applicable to a large class of quantum integrable models.
Highlights
The description of the collective motion in many-body quantum systems is one of the most challenging problems in theoretical physics
Our exact formula has a simple semiclassical interpretation: The currents can be computed by summing over the charge eigenvalues carried by the individual bare particles, multiplied with an effective velocity describing their propagation in the presence of the other particles
The timescales of equilibration to the generalized Gibbs ensemble (GGE) are set by the microscopic laws. It follows that in mesoscopic or macroscopic dynamical processes, local equilibration happens much sooner than the characteristic times of the transport processes. This separation of timescales leads to the hydrodynamic description: Generalized hydrodynamics (GHD) assumes the existence of fluid cells such that the state of each fluid cell can be described by a local GGE
Summary
The description of the collective motion in many-body quantum systems is one of the most challenging problems in theoretical physics. For arbitrary current operators in interacting lattice models or nonrelativistic gases (the models most relevant to experiments), it was completely missing up to now It is the goal of this paper to provide a proof of the conjecture valid for a wide class of Bethe ansatz solvable models. The current operators are very specific short-range objects, and as we show, their finite-volume mean values take a remarkably simple form. This result has not yet been noticed in the Bethe ansatz literature, and we believe that it deserves a study in its own right.
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