SciPost Phys. 9, 040 (2020) ·
published 15 September 2020
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.
SciPost Phys. 3, 039 (2017) ·
published 15 December 2017
Based on the method of hydrodynamic projections we derive a concise formula
for the Drude weight of the repulsive Lieb-Liniger $\delta$-Bose gas. Our
formula contains only quantities which are obtainable from the thermodynamic
Bethe ansatz. The Drude weight is an infinite-dimensional matrix, or bilinear
functional: it is bilinear in the currents, and each current may refer to a
general linear combination of the conserved charges of the model. As a
by-product we obtain the dynamical two-point correlation functions involving
charge and current densities at small wavelengths and long times, and in
addition the scaled covariance matrix of charge transfer. We expect that our
formulas extend to other integrable quantum models.