Current operators in integrable models: A review

Abstract

We consider the current operators of one dimensional integrable models. These operators describe the flow of the conserved charges of the models, and they play a central role in Generalized Hydrodynamics. We present the key statements about the mean currents in finite volume and in the thermodynamic limit, and we review the various proofs of the exact formulas. We also present a few new results in this review. New contributions include a computation of the currents of the Heisenberg spin chains using the string hypothesis, and simplified formulas in the thermodynamic limit. We also discuss implications of our results for the asymptotic behaviour of dynamical correlation functions.

arXiv comment38 pages, to be submitted to the special issue of Journal of Statistical Mechanics on Emergent Hydrodynamics in Integrable Many-body Systems

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Cited by in corpus (16)

• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Hydrodynamics of weak integrability breaking
• Ballistic macroscopic fluctuation theory
• Form factors and generalized hydrodynamics for integrable systems
• Fragmentation and emergent integrable transport in the weakly tilted Ising chain
• Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation
• Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model
• A Yang-Baxter integrable cellular automaton with a four site update rule
• The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
• The hydrodynamic theory of dynamical correlation functions in the XX chain
• The dissipative Generalized Hydrodynamic equations and their numerical solution
• All Local Conserved Quantities of the One-Dimensional Hubbard Model
• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
• Nonequilibrium symmetry-protected topological order: emergence of semilocal Gibbs ensembles
• Benchmarks of Generalized Hydrodynamics for 1D Bose Gases
• Current mean values in the XYZ model