The spin Drude weight of the XXZ chain and generalized hydrodynamics

Abstract

Based on a generalized free energy we derive exact thermodynamic Bethe ansatz formulas for the expectation value of the spin current, the spin current-charge, charge-charge correlators, and consequently the Drude weight. These formulas agree with recent conjectures within the generalized hydrodynamics formalism. They follow, however, directly from a proper treatment of the operator expression of the spin current. The result for the Drude weight is identical to the one obtained 20 years ago based on the Kohn formula and TBA. We numerically evaluate the Drude weight for anisotropies $\Delta =\cos (\gamma )$ with $\gamma =n\pi /m$, $n\le m$ integer and coprime. We prove, furthermore, that the high-temperature asymptotics for general $\gamma =\pi n/m$---obtained by analysis of the quantum transfer matrix eigenvalues---agrees with the bound which has been obtained by the construction of quasi-local charges.

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Cited by in corpus (46)

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• Diffusion in generalized hydrodynamics and quasiparticle scattering
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• Ballistic spin transport in a periodically driven integrable quantum system
• Diffusive hydrodynamics from integrability breaking
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• Free fermions at the edge of interacting systems
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• Weak integrability breaking and level spacing distribution
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• The GGE averaged currents of the classical Toda chain
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• Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
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• Charge-current correlation equalities for quantum systems far from equilibrium
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• Benchmarks of Generalized Hydrodynamics for 1D Bose Gases
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory
• The Staircase Model: Massless Flows and Hydrodynamics
• The Theory of Generalised Hydrodynamics for the One-dimensional Bose Gas
• Non-linear Transport by Bethe Bound States
• Spin Drude weight for the integrable XXZ chain with arbitrary spin
• Dressed excitations, thermodynamics and relaxation in the 1D XXZ Heisenberg model
• Wavelet representation of hardcore bosons
• Thermal Drude weight in an integrable chiral clock model
• The Bloch theorem in the presence of an additional conserved charge