Tue, 13 Feb 2024
16:00 - 17:00
Leonid Pastur
King's College London / B. Verkin Institute for Low Temperature Physics and Engineering

We consider a macroscopic system of free lattice fermions, and we are interested in the entanglement entropy (EE) of a large block of size L of the system, treating the rest of the system as the macroscopic environment of the block. Entropy is a widely used quantifier of quantum correlations between a block and its surroundings. We begin with known results (mostly one-dimensional) on the asymptotics form of EE of translation-invariant systems for large L, where for any value of the Fermi energy there are basically two asymptotics known as area law and enhanced (violated ) area law. We then show that in the disordered case and for the Fermi energy belonging to the localized spectrum of a one-body Hamiltonian, the EE obeys the area law for all typical realizations of disorder and any dimension. As for the enhanced area law, it turns out to be possible for some special values of the Fermi energy in the one-dimensional case

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