Entanglement Rényi entropies from Ballistic Fluctuations Theory: the free fermionic case

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• Paola Ruggiero, Kings College London
• Thursday 30 May 2024, 14:00-15:00
• TCM Seminar Room.

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Recently, a new framework dubbed Ballistic Fluctuation Theory (BFT) has been proposed, which gives access to the full statistics of fluctuations of ballistically transported conserved quantities within homogeneous, stationary states [1]. The formalism, based on large deviation theory (LDT), is expected to apply to generic one-dimensional systems with an Euler hydrodynamic description. One of its most interesting application is to correlation functions of twist fields, which can be introduced any time the system possesses a symmetry. A particularly important example are branch-point twist fields associated to the Zn symmetry in a n-copies replicated theory, whose correlations functions provide the starting point for computing Rényi entanglement entropies within the replica approach [2]. In this talk, focusing on free fermionic systems, we apply the formalism to correlation functions of branch-point twist fields and show that both the equilibrium behavior and the dynamics of Renyi entanglement entropies can be simply derived from a unique formula, thus providing a unified interpretation of the two results [3].

Refs: [1] Doyon, Myers, “Fluctuations in ballistic transport from Euler hydrodynamics”, J. Ann. Henri Poincaré 21, 255-302 (2020) [2] Calabrese, Cardy, “Entanglement Entropy and Quantum Field Theory”, J. Stat. Mech. P06002 (2004) [3] Del Vecchio Del Vecchio, Doyon, Ruggiero, SciPost Phys. Core 7, 005 (2024)

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