Göttingen 2025 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 11: Quantum Field Theory II
MP 11.2: Vortrag
Donnerstag, 3. April 2025, 16:35–16:55, ZHG001
Large deviations in mean-field quantum spin systems — •Christiaan van de Ven1 and Matthias Keller2 — 1Weierstraße 52, 52349 Düren — 2Institut für Mathematik, Universität Potsdam, Karl-Liebknecht-Straße 24-25, 14476 Potsdam
Continuous fields of C*-algebras form an important ingredient for describing emergent phenomena, such as phase transitions and spontaneous symmetry breaking. In this talk, I consider the continuous C*-bundle generated by increasing symmetric tensor powers of the complex (lxl) matrices, which can be interpreted as abstract description of mean-field theories defining the macroscopic limit of infinite quantum systems. Within this framework I discuss the principle of large deviations for the local Gibbs state in the high temperature regime and characterize the limit of the ensuing logarithmic generating function. To this end, it has proved necessary to demonstrate the existence of a semiclassical analog of the Baker-Campbel-Hausdorff formula, defined in terms of a series of nested Poisson brackets.
Keywords: Large deviations; Statistical mechanics; Operator algebras; Continuous field of C*-algebras; Mean-field quantum spin systems