The spin Drude weight of the spin-1/2 $XXZ$ chain: An analytic finite size study

Abstract

The Drude weight for the spin transport of the spin-1/2 $XXZ$ Heisenberg chain in the critical regime is evaluated exactly for finite temperatures. We combine the thermodynamic Bethe ansatz with the functional relations of type $Y$-system satisfied by the row-to-row transfer matrices. This makes it possible to evaluate the asymptotic behavior of the finite temperature spin Drude weight with respect to the system size. As a result, the Drude weight converges to the results obtained by Zotos (Phys. Rev. Lett. 82, 1764 (1999)), however with very slow convergence upon increase of the system size. This strong size dependence may explain that extrapolations from various numerical approaches yield conflicting results.

arXiv comment16 pages, Submission to SciPost

References in corpus (21)

• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Transport and conservation laws
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Quasilocal charges in integrable lattice systems
• Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
• Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain
• Diffusion and ballistic transport in one-dimensional quantum systems
• Families of quasi-local conservation laws and quantum spin transport
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Microscopic origin of ideal conductivity in integrable quantum models
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Zero-frequency transport properties of one dimensional spin-1/2 systems
• The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• On the finite temperature Drude weight of the anisotropic Heisenberg chain
• Low-temperature transport in Heisenberg chains
• Exact Drude weight for the one-dimensional Hubbard model at finite temperatures
• Finite-temperature Drude weight within the anisotropic Heisenberg chain
• Thermomagnetic Power and Figure of Merit for Spin-1/2 Heisenberg Chain
• Finite Drude weight for 1D low temperature conductors
• Non-dissipative Thermal Transport and Magnetothermal Effect for the Spin-1/2 Heisenberg Chain

Cited by in corpus (4)

• Finite-temperature transport in one-dimensional quantum lattice models
• Kubo's response theory and bosonization with a background gauge field and irrelevant perturbations
• Spin Drude weight for the integrable XXZ chain with arbitrary spin
• Dressed excitations, thermodynamics and relaxation in the 1D XXZ Heisenberg model