Large Deviations in Weakly Interacting Fermions -- Generating Functions as Gaussian Berezin Integrals and Bounds on Large Pfaffians
| Autor: | Walter de Siqueira Pedra, L. C. P. A. M. Müssnich, Jean-Bernard Bru, N. J. B. Aza |
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| Rok vydání: | 2021 |
| Předmět: |
Physics
Berezin integral Gaussian Lattice (group) Generating function FOS: Physical sciences Statistical and Nonlinear Physics Fermion Mathematical Physics (math-ph) large deviations symbols.namesake interacting fermions symbols Probability distribution Large deviations theory Limit (mathematics) constructive methods determinant bound 81T08 82C22 46L53 Mathematical Physics Pfaffian bound Mathematical physics |
| Zdroj: | BIRD: BCAM's Institutional Repository Data instname |
| DOI: | 10.48550/arxiv.2105.13308 |
| Popis: | We prove that the G\"{a}rtner--Ellis generating function of probability distributions associated with KMS states of weakly interacting fermions on the lattice can be written as the limit of logarithms of Gaussian Berezin integrals. The covariances of the Gaussian integrals are shown to have a uniform Pfaffian bound and to be summable in general cases of interest, including systems that are \emph{not} translation invariant. The Berezin integral representation can thus be used to obtain convergent expansions of the generating function in terms of powers of its parameter. The derivation and analysis of the expansions of logarithms of Berezin integrals are the subject of the second part of the present work. Such technical results are also useful, for instance, in the context of quantum information theory, in the computation of relative entropy densities associated with fermionic Gibbs states, and in the theory of quantum normal fluctuations for weakly interacting fermion systems. FAPESP (2017/22340-9) CNPq (309723/2020-5) by the Basque Government through the grant IT641-13 MTM2017-82160-C2-2-P. |
| Databáze: | OpenAIRE |
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