2024/04/10 by Fabrizio Ferro, Ferro, Fabrizio, Wolfgang Spitzer +2
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum many-body systems #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2404.07068
openalex publication_date 2024/04/10 · openalex created_date 2024/04/12 · openalex updated_date 2026/07/28
We present a novel proof of a formula of Casini and Huerta for the entanglement entropy of the ground state of non-interacting massless Dirac fermions in dimension one localized to (a union of) intervals and generalize it to the case of Rényi entropies. At first, we prove that these entropies are well-defined for non-intersecting intervals. This is accomplished by an inequality of Alexander V.~Sobolev. Then we compute this entropy using a trace formula for Wiener--Hopf operators by Harold Widom. For intersecting intervals, we discuss an extended entropy formula of Casini and Huerta and support this with a proof for polynomial test functions (instead of entropy).