Maximilian KieferEmmanouilidis, Razmik Unanyan, Jesko Sirker, Michael Fleischhauer
SciPost Phys. 8, 083 (2020) ·
published 3 June 2020

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Entanglement in a pure state of a manybody system can be characterized by the R\'enyi entropies $S^{(\alpha)}=\ln\textrm{tr}(\rho^\alpha)/(1\alpha)$ of the reduced density matrix $\rho$ of a subsystem. These entropies are, however, difficult to access experimentally and can typically be determined for small systems only. Here we show that for free fermionic systems in a Gaussian state and with particle number conservation, $\ln S^{(2)}$ can be tightly boundfrom above and belowby the much easier accessible R\'enyi number entropy $S^{(2)}_N=\ln \sum_n p^2(n)$ which is a function of the probability distribution $p(n)$ of the total particle number in the considered subsystem only. A dynamical growth in entanglement, in particular, is therefore always accompanied by a growthalbeit logarithmically slowerof the number entropy. We illustrate this relation by presenting numerical results for quenches in noninteracting onedimensional lattice models including disorderfree, Andersonlocalized, and critical systems with offdiagonal disorder.
Andrew Urichuk, Yahya Oez, Andreas Klümper, Jesko Sirker
SciPost Phys. 6, 005 (2019) ·
published 11 January 2019

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Based on a generalized free energy we derive exact thermodynamic Bethe ansatz
formulas for the expectation value of the spin current, the spin
currentcharge, chargecharge 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 $\gamma = n\pi/m$, $n\leq m$ integer and coprime. We
prove, furthermore, that the hightemperature asymptotics for general
$\gamma=\pi n/m$obtained by analysis of the quantum transfer matrix
eigenvaluesagrees with the bound which has been obtained by the construction
of quasilocal charges.
Submissions
Submissions for which this Contributor is identified as an author:
Prof. Sirker: "In the second report, the refe..."
in Report on Transport in onedimensional integrable quantum systems