Dynamical mean-field theory for Rényi entanglement entropy and mutual Information in Hubbard Model

Abstract

Quantum entanglement, lacking any classical counterpart, provides a fundamental new route to characterize the quantum nature of many-body states. In this work, we discuss an implementation of a new path integral method [Phys. Rev. Res. 2, 033505 (2020)] for fermions to compute entanglement for extended subsystems in the Hubbard model within dynamical mean field theory (DMFT) in one and two dimensions. The new path integral formulation measures entanglement by applying a ``kick" to the underlying interacting fermions. We show that the Rényi entanglement entropy can be extracted efficiently within the DMFT framework by integrating over the strength of the kick term. Using this method, we compute the second Rényi entropy as a function of subsystem size for metallic and Mott insulating phases of the Hubbard model. We explore the thermal entropy to entanglement crossover in the subsystem Rényi entropy in the correlated metallic phase. We show that the subsystem-size scaling of second Rényi entropy is well described by the crossover formula which interpolates between the volume-law thermal Rényi entropy and the universal boundary-law Rényi entanglement entropy with logarithmic violation, as predicted by conformal field theory. We also study the mutual information across the Mott metal-insulator transition.

13 pages, 12 figures

References in corpus (19)

• Many body localization and thermalization in quantum statistical mechanics
• Continuous-time Monte Carlo methods for quantum impurity models
• Area laws in quantum systems: mutual information and correlations
• On the quantum, classical and total amount of correlations in a quantum state
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Random Quantum Circuits
• Cluster Dynamical Mean Field Theory of the Mott Transition
• Entanglement Entropy in the O(N) model
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Finite Temperature Critical Behavior of Mutual Information
• Cellular Dynamical Mean Field Theory for the 1D Extended Hubbard Model
• Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions
• Entanglement entropy of the $\nu =1/2$ composite fermion non-Fermi liquid state
• Renyi Entanglement Entropy of Interacting Fermions Calculated Using Continuous-Time Quantum Monte Carlo Method
• Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations
• Dynamical Mean Field Theory of Moiré Bilayer Transition Metal Dichalcogenides: Phase Diagram, Resistivity, and Quantum Criticality
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Momentum space entanglement of interacting fermions
• Entanglement Spectrum in Cluster Dynamical Mean-Field Theory

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• Information scrambling and butterfly velocity in quantum spin glass chains