SciPost Physics

SciPost Phys. 9, 040 (2020) · published 15 September 2020

• doi: 10.21468/SciPostPhys.9.3.040
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Abstract

For quantum integrable systems the currents averaged with respect to a generalized Gibbs ensemble are revisited. An exact formula is known, which we call “collision rate ansatz”.While there is considerable work to confirm this ansatz in various models, our approach uses the symmetry of the current-charge susceptibility matrix, which holds in great generality. Besides some technical assumptions, the main input is the availability of a self-conserved current, i.e. some current which is itself conserved. The collision rate ansatz is then derived. The argument is carried out in detail for the Lieb-Liniger model and the Heisenberg XXZ chain. The Fermi-Hubbard is not covered, since no self-conserved current seems to exist. It is also explained how from the existence of a boost operator a self-conserved current can be deduced.

• Durnin et al., Diffusive hydrodynamics of inhomogenous Hamiltonians
  J. Phys. A: Math. Theor. 54, 494001 (2021) [Crossref]
• Borsi et al., Current operators in integrable models: a review
  J. Stat. Mech. 2021, 094001 (2021) [Crossref]
• Bulchandani et al., Superdiffusion in spin chains
  J. Stat. Mech. 2021, 084001 (2021) [Crossref]
• Gopalakrishnan et al., Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems
  Annu. Rev. Condens. Matter Phys. 15, 159 (2024) [Crossref]
• Cardy et al., $$ T\overline{T} $$ deformations and the width of fundamental particles
  J. High Energ. Phys. 2022, 136 (2022) [Crossref]
• Møller et al., Euler-scale dynamical correlations in integrable systems with fluid motion
  SciPost Phys. Core 3, 016 (2020) [Crossref]
• Jiang, $\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas
  SciPost Phys. 12, 191 (2022) [Crossref]
• Bastianello et al., Thermalization of a Trapped One-Dimensional Bose Gas via Diffusion
  Phys. Rev. Lett. 125, 240604 (2020) [Crossref]
• Fukai, All Local Conserved Quantities of the One-Dimensional Hubbard Model
  Phys. Rev. Lett. 131, 256704 (2023) [Crossref]
• Scopa et al., Generalized hydrodynamics of the repulsive spin- 12 Fermi gas
  Phys. Rev. B 106, 134314 (2022) [Crossref]
• De Nardis et al., Hydrodynamic gauge fixing and higher order hydrodynamic expansion
  J. Phys. A: Math. Theor. 56, 245001 (2023) [Crossref]
• Perfetto et al., Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
  SciPost Phys. 10, 116 (2021) [Crossref]
• Bonnemain et al., Generalized hydrodynamics of the KdV soliton gas
  J. Phys. A: Math. Theor. 55, 374004 (2022) [Crossref]
• Sakbaev, Flows in Infinite-Dimensional Phase Space Equipped with a Finitely-Additive Invariant Measure
  Mathematics 11, 1161 (2023) [Crossref]
• Bastianello et al., Hydrodynamics of weak integrability breaking
  J. Stat. Mech. 2021, 114003 (2021) [Crossref]
• Bulchandani et al., Quasiparticle kinetic theory for Calogero models
  J. Phys. A: Math. Theor. 54, 474001 (2021) [Crossref]
• Doyon et al., The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
  SciPost Phys. 13, 072 (2022) [Crossref]
• Del Vecchio Del Vecchio et al., The hydrodynamic theory of dynamical correlation functions in the XX chain
  J. Stat. Mech. 2022, 053102 (2022) [Crossref]
• Zadnik et al., The folded spin-1/2 XXZ model: II. Thermodynamics and hydrodynamics with a minimal set of charges
  SciPost Phys. 10, 099 (2021) [Crossref]
• Medenjak et al., Thermal transport in TT¯ -deformed conformal field theories: From integrability to holography
  Phys. Rev. D 103, 066012 (2021) [Crossref]
• Cubero et al., Form factors and generalized hydrodynamics for integrable systems
  J. Stat. Mech. 2021, 114002 (2021) [Crossref]
• Bertini et al., Finite-temperature transport in one-dimensional quantum lattice models
  Rev. Mod. Phys. 93, 025003 (2021) [Crossref]
• Alba et al., Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects
  J. Stat. Mech. 2021, 114004 (2021) [Crossref]
• Mazzuca et al., Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale
  J Stat Phys 190, 149 (2023) [Crossref]
• Lopez-Piqueres et al., Hydrodynamics of nonintegrable systems from a relaxation-time approximation
  Phys. Rev. B 103, L060302 (2021) [Crossref]
• Mazzoni et al., The staircase model: massless flows and hydrodynamics
  J. Phys. A: Math. Theor. 54, 404005 (2021) [Crossref]
• Bouchoule et al., Generalized hydrodynamics in the one-dimensional Bose gas: theory and experiments
  J. Stat. Mech. 2022, 014003 (2022) [Crossref]