Random Matrix Model for the Entanglement Entropy of Free Fermions

Watch this 38-minute scientific lecture exploring quantum entanglement through the lens of random matrix theory for free fermion systems. Delve into the mathematical analysis of entanglement entropy, focusing on the relationship between subsystem (block) size L and total system size N. Learn how the traditional approach of successive limits (N → ∞ followed by L → ∞) compares to simultaneous limits where L and N grow proportionally. Examine how free fermions in their ground state, governed by a random matrix one-body Hamiltonian, demonstrate volume law behavior typically associated with mixed states or highly excited pure states. Presented by Leonid Pastur from King's College London at the Institut des Hautes Etudes Scientifiques (IHES), this lecture bridges quantum mechanics, statistical physics, and random matrix theory to provide insights into quantum correlations and entanglement properties.