# Regensburg 2019 – wissenschaftliches Programm

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# TT: Fachverband Tiefe Temperaturen

## TT 30: Correlated Electrons: 1D Theory

### TT 30.7: Vortrag

### Dienstag, 2. April 2019, 15:30–15:45, H4

**The spin Drude weight of the XXZ chain and generalized hydrodynamics** — •Yahya Öz^{1}, Andrew Urichuk^{2}, Andreas Klümper^{1}, and Jesko Sirker^{2} — ^{1}Bergische Universität Wuppertal, Deutschland — ^{2}University of Manitoba, Canada

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 Δ=cosγ with γ=π *n*/*m*,
*n*≤ *m* integer and coprime. We prove, furthermore, that the high-temperature
asymptotics for general γ=π *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.