Correlation functions and transport coefficients in generalised hydrodynamics

Abstract

We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights, conductivity and diffusion constants, as well as linear and nonlinear response on top of equilibrium and non-equilibrium states. We consider the problems from the complementary perspectives of the general hydrodynamic theory of many-body systems, including hydrodynamic projections, and form-factor expansions in integrable models, and show how they provide a comprehensive and consistent set of exact methods to extract large scale behaviours. Finally, we overview various applications in integrable spin chains and field theories.

93 pages, 16 figures. To appear in JSTAT special issue "Emergent Hydrodynamics in Integrable Many-body Systems"

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Cited by in corpus (64)

• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Hydrodynamics of weak integrability breaking
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Ballistic macroscopic fluctuation theory
• Absence of Normal Fluctuations in an Integrable Magnet
• Anomalous transport from hot quasiparticles in interacting spin chains
• Fragmentation and emergent integrable transport in the weakly tilted Ising chain
• Generalized hydrodynamics: a perspective
• Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation
• Universal anomalous fluctuations in charged single-file systems
• Translation symmetry restoration under random unitary dynamics
• Hydrodynamic gauge fixing and higher order hydrodynamic expansion
• Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains
• Diffusive Hydrodynamics of Inhomogenous Hamiltonians
• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• Entropy growth during free expansion of an ideal gas
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
• Probing the local rapidity distribution of a 1D Bose gas
• The hydrodynamic theory of dynamical correlation functions in the XX chain
• The dissipative Generalized Hydrodynamic equations and their numerical solution
• BBGKY Hierarchy and Generalised Hydrodynamics
• Thermodynamics and fractal Drude weights in the sine-Gordon model
• Exact large-scale fluctuations of the phase field in the sine-Gordon model
• Scaling of fronts and entanglement spreading during a domain wall melting
• Large-scale universality in quantum reaction-diffusion from Keldysh field theory
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Nonlinear Response in Diffusive Systems
• Popcorn Drude weights from quantum symmetry
• Integrability breaking in the Rule 54 cellular automaton
• Current correlations, Drude weights and large deviations in a box-ball system
• New classical integrable systems from generalized $T\bar{T}$-deformations
• Integrability breaking from backscattering
• Nonequilibrium symmetry-protected topological order: emergence of semilocal Gibbs ensembles
• Spin conductivity of the XXZ chain in the antiferromagnetic massive regime
• Navier-Stokes equations for nearly integrable quantum gases
• Characterising transport in a quantum gas by measuring Drude weights
• Benchmarks of Generalized Hydrodynamics for 1D Bose Gases
• Finite temperature spin diffusion in the Hubbard model in the strong coupling limit
• Landau-Lifschitz magnets: exact thermodynamics and transport
• Quantum many-body spin ratchets
• Thermodynamic Bethe Ansatz and Generalised Hydrodynamics in the sine-Gordon model
• Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case
• Long-time dynamics in quantum spin lattices: ergodicity and hydrodynamic projections at all frequencies and wavelengths
• Connected correlations in partitioning protocols: a case study and beyond
• Subdiffusive transport in the Fredkin dynamical universality class
• Disorder-Order Interface Propagating over the Ferromagnetic Ground State in the Transverse Field Ising Chain
• The relevant excitations for the one-body function in the Lieb-Liniger model
• Prethermalization in coupled one-dimensional quantum gases
• Identifying diffusive length scales in one-dimensional Bose gases
• Dynamical separation of charge and energy transport in one-dimensional Mott insulators
• Experimental Investigation of a Bipartite Quench in a 1D Bose gas
• Integrability and charge transport in asymmetric quantum-circuit geometries
• Non-linear Transport by Bethe Bound States
• Spin Drude weight for the integrable XXZ chain with arbitrary spin
• A hydrodynamic approach to Stark localization
• Kinetics of Quantum Reaction-Diffusion systems
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Quest for the golden ratio universality class
• Anomalous charge transport in the sine-Gordon model
• Observation of a generalized Gibbs ensemble in photonics
• Extending the Thermodynamic Form Factor Bootstrap Program: Multiple particle-hole excitations, crossing symmetry, and reparameterization invariance
• Universal scaling of higher-order cumulants in quantum isotropic spin chains
• Macroscopic Quantum States and Universal Correlations in a Disorder-Order Interface Propagating over a 1D Ground State