Leschke, H;
Sobolev, AV;
Spitzer, W;
(2017)
Trace formulas for Wiener-Hopf operators with applications to entropies of free fermionic equilibrium states.
Journal of Functional Analysis
, 273
(3)
pp. 1049-1094.
10.1016/j.jfa.2017.04.005.
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Abstract
We consider non-smooth functions of (truncated) Wiener–Hopf type operators on the Hilbert space L2(Rd) . Our main results are uniform estimates for trace norms ( d≥1 ) and quasiclassical asymptotic formulas for traces of the resulting operators ( d=1 ). Here, we follow Harold Widom's seminal ideas, who proved such formulas for smooth functions decades ago. The extension to non-smooth functions and the uniformity of the estimates in various (physical) parameters rest on recent advances by one of the authors (AVS). We use our results to obtain the large-scale behaviour of the local entropy and the spatially bipartite entanglement entropy (EE) of thermal equilibrium states of non-interacting fermions in position space Rd ( d≥1 ) at positive temperature, T>0 . In particular, our definition of the thermal EE leads to estimates that are simultaneously sharp for small T and large scaling parameter α>0 provided that the product Tα remains bounded from below. Here α is the reciprocal quasiclassical parameter. For d=1 we obtain for the thermal EE an asymptotic formula which is consistent with the large-scale behaviour of the ground-state EE (at T=0 ), previously established by the authors for d≥1 .
Type: | Article |
---|---|
Title: | Trace formulas for Wiener-Hopf operators with applications to entropies of free fermionic equilibrium states |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1016/j.jfa.2017.04.005 |
Publisher version: | https://doi.org/10.1016/j.jfa.2017.04.005 |
Language: | English |
Additional information: | Copyright © 2017 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | Science & Technology, Physical Sciences, Mathematics, Non-smooth functions of Wiener-Hopf operators, Asymptotic trace formulas, Entanglement entropy |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
URI: | https://discovery.ucl.ac.uk/id/eprint/1563833 |
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