Dynamical mean-field theory for Rényi entanglement entropy and mutual Information in Hubbard Model
arXiv:2302.10940 · doi:10.1103/PhysRevB.109.035156
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.
arXiv comment13 pages, 12 figures
References in corpus (72)
- A computable measure of entanglement
- Entanglement Entropy and Quantum Field Theory
- Area laws for the entanglement entropy - a review
- Entanglement in quantum critical phenomena
- Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
- Topological entanglement entropy
- Many body localization and thermalization in quantum statistical mechanics
- Detecting topological order in a ground state wave function
- Aspects of Holographic Entanglement Entropy
- Many-body localization, thermalization, and entanglement
- Geometric and Renormalized Entropy in Conformal Field Theory
- Entanglement entropy and conformal field theory
- Continuous-time Monte Carlo methods for quantum impurity models
- Quantum Cluster Theories
- Nonequilibrium dynamical mean-field theory and its applications
- Quantum entanglement in condensed matter systems
- Area laws in quantum systems: mutual information and correlations
- Cellular Dynamical Mean Field Approach to Strongly Correlated Systems
- Entanglement entropy in free quantum field theory
- On the quantum, classical and total amount of correlations in a quantum state
- Entanglement entropy of fermions in any dimension and the Widom conjecture
- Universal dynamics and renormalization in many body localized systems
- Random Quantum Circuits
- Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
- Universality of Entropy Scaling in 1D Gap-less Models
- The Dynamical Cluster Approximation: Non-Local Dynamics of Correlated Electron Systems
- Cluster Dynamical Mean Field Theory of the Mott Transition
- Parity effects in the scaling of block entanglement in gapless spin chains
- Entanglement Entropy and the Fermi Surface
- Entanglement Entropy in the O(N) model
- Density Operators for Fermions
- Landau Theory of the Finite Temperature Mott Transition
- Emergent conformal symmetry in non-unitary random dynamics of free fermions
- Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions
- Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
- Quantum Entanglement of Interacting Fermions in Monte Carlo
- Finite Size Scaling of Mutual Information: A Scalable Simulation
- Cluster Dynamical Mean-Field Theory of the density-driven Mott transition in the one-dimensional Hubbard model
- Scaling of Rényi entanglement entropies of the free Fermi-gas ground state: a rigorous proof
- Universal crossovers between entanglement entropy and thermal entropy
- Hidden Fermi Liquid, Scattering Rate Saturation and Nernst Effect: a DMFT Perspective
- Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
- Entanglement entropies in free fermion gases for arbitrary dimension
- Finite Temperature Critical Behavior of Mutual Information
- Cellular Dynamical Mean Field Theory for the 1D Extended Hubbard Model
- Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization
- Entanglement entropy from nonequilibrium work
- The Hubbard model on the honeycomb lattice: from static and dynamical mean-field theories to lattice quantum Monte Carlo simulations
- Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions
- Detecting Classical Phase Transitions with Renyi Mutual Information
- Entanglement entropy of the composite fermion non-Fermi liquid state
- Renyi Entanglement Entropy of Interacting Fermions Calculated Using Continuous-Time Quantum Monte Carlo Method
- Entanglement entropy and mutual information across the Mott transition in the two-dimensional Hubbard model
- 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 Wilson-Fisher conformal field theory
- Renyi entropy, mutual information, and fluctuation properties of Fermi liquids
- Conformal Field Theory on the Fermi Surface
- Subsystem Rényi Entropy of Thermal Ensembles for SYK-like models
- Quantum Monte Carlo Study of Strongly Correlated Electrons: Cellular Dynamical Mean-Field Theory
- Thermodynamic and information-theoretic description of the Mott transition in the two-dimensional Hubbard model
- Geometric mutual information at classical critical points
- Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
- Entanglement Entropy and its Quench Dynamics for Pure States of the Sachdev-Ye-Kitaev model
- Oscillating terms in the Renyi entropy of Fermi liquids
- Entanglement and classical correlations at the doping-driven Mott transition in the two-dimensional Hubbard model
- Fractionalized Excitations Revealed by Entanglement Entropy
- Entanglement Entropy of Fermions from Wigner Functions: Excited States and Open Quantum Systems
- Renyi Entropy of Interacting Thermal Bosons in Large Approximation
- Momentum space entanglement of interacting fermions
- Entanglement Spectrum in Cluster Dynamical Mean-Field Theory
- Non-equilibrium Dynamics of Renyi Entropy for Bosonic Many-Particle Systems
Cited by in corpus (5)
- Quasilocal entanglement across the Mott-Hubbard transition
- Entanglement in the pseudogap regime of cuprate superconductors
- Mott metal-insulator transition in a modified periodic Anderson model: Insights from entanglement entropy and role of short-range spatial correlations
- Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model
- Information scrambling and butterfly velocity in quantum spin glass chains