2025/10/16 by Mrinal Kanti Sarkar, Sarkar, Mrinal Kanti, Saranyo Moitra +3
Computer Science · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Other Condensed Matter (cond-mat.other) #Quantum Gases (cond-mat.quant-gas) #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2510.15035
openalex publication_date 2025/10/16 · openalex created_date 2025/10/21 · openalex updated_date 2026/07/28
We show that odd order Rényi entropies S(2q+1) of a system of interacting scalar fields can be calculated as the free energy of 2q+1 replicas of the system with additional quadratic inter-replica couplings in the subsystem at the time of measurement of the entropy. These couplings replace boundary field matching conditions. This formalism works both in and out of thermal equilibrium, for closed as well as open quantum systems, and provides a general dictionary between measurable correlation functions and entanglement entropy. S(2q+1) can be analytically continued to calculate the von Neumann entropy SvN. We provide an exact formula relating S(2q+1) and SvN with correlation functions in a non-interacting theory. For interacting theories, we provide rules for constructing all possible Feynman diagrams for S(2q+1). We show that the boundary matching conditions cannot be completely eliminated while calculating Rényi entropies of even order due to presence of zero modes in replica space.