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.

Fragmentation and emergent integrable transport in the weakly tilted Ising chain

“…Using Generalized Hydrodynamics (GHD) [39,40] (see also Refs. [41][42][43][44][45][46]) we analytically tackle transport within the isolated magnon sector. Since the Alcaraz-Bariev (AB) model is a close relative of the XXZ spin chain, it inherits its rich phenomenology: transport greatly depends on the interactions and can exhibit sharp jumps [47].…”

“…Here we focus on transport in the AB model and arbitrary ∆. Being integrable, the AB model possesses an extensive number of (quasi-)local conserved quantities [56], with striking consequences on its nonequilibrium features, hindering thermalization [57] and featuring ballistic transport [41]. The AB Hilbert space is made of multiparticle magnonic asymptotic states labeled by the set of rapidities {λ j } N j=1 , which generalize the momenta of non-interacting systems.…”

Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation

“…This result has first been obtained for the time independent and homogeneous GGEs [109] and was tested for the first time on the classical Sinh Gordon model [70]. Later, expressions for inhomogeneous and time dependent GGEs became available [110] (see also [38]). For simplicity, here we focus on the two-point correlation of the density on constant GGEs…”

Anisotropic Landau-Lifshitz Model in Discrete Space-Time

“…Refs. [41,88]). As customary, we define the dynamical structure factor S( , t) = q( , t) q(0, 0) c µ , (…”

“…Concurrently, we have seen an increased theoretical interest in various facets of nonequilibrium physcis. Integrable systems have been in the spotlight lately [13][14][15][16][17][18][19][20][21][22][23], largely due to their inherent non-ergodic features [24][25][26][27] and anomalous transport properties [5,[28][29][30][31][32][33][34][35][36][37][38] as recently covered in a compilation of review articles [39][40][41][42][43][44]. The study of nonequilibrium properties in classical integrable dynamical systems of interacting particles or fields has received comparatively less attention [45][46][47][48][49][50][51][52].…”