Unlocking the general relationship between energy and entanglement spectra via the wormhole effect

Abstract

Based on the path integral formulation of the reduced density matrix, we develop a scheme to overcome the exponential growth of computational complexity in reliably extracting low-lying entanglement spectrum from quantum Monte Carlo simulations. We test the method on the Heisenberg spin ladder with long entangled boundary between two chains and the results support the Li and Haldane's conjecture on entanglement spectrum of topological phase. We then explain the conjecture via the wormhole effect in the path integral and show that it can be further generalized for systems beyond gapped topological phases. Our further simulation results on the bilayer antiferromagnetic Heisenberg model with 2D entangled boundary across the $(2+1)$D O(3) quantum phase transition clearly demonstrate the correctness of the wormhole picture. Finally, we state that since the wormhole effect amplifies the bulk energy gap by a factor of $\beta$, the relative strength of that with respect to the edge energy gap will determine the behavior of low-lying entanglement spectrum of the system.

arXiv comment9 pages, 5 figures

References in corpus (85)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum of a topological phase in one dimension
• Quantum Monte Carlo with Directed Loops
• Quantum entanglement in condensed matter systems
• Stochastic series expansion method with operator-loop update
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Universality of Entropy Scaling in 1D Gap-less Models
• Entanglement spectrum in one-dimensional systems
• Entanglement spectrum of topological insulators and superconductors
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• A symmetry principle for Topological Quantum Order
• Entanglement spectrum and boundary theories with projected entangled-pair states
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
• Universal terms for the entanglement entropy in 2+1 dimensions
• Symmetry and Topological Order
• High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers
• Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
• Non-local order in gapless systems: Entanglement Spectrum in Spin Chains
• Entanglement spectra of quantum Heisenberg ladders
• Determining a local Hamiltonian from a single eigenstate
• Quantum Simulation and Spectroscopy of Entanglement Hamiltonians
• Universal behavior beyond multifractality in quantum many-body systems
• Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
• Quantum Entanglement of Interacting Fermions in Monte Carlo
• Constrained sampling method for analytic continuation
• Entanglement at a Two-Dimensional Quantum Critical Point: a Numerical Linked Cluster Expansion Study
• How universal is the entanglement spectrum?
• Kosterlitz-Thouless Melting of Magnetic Order in the Triangular Quantum Ising Material TmMgGaO${}_4$
• Scaling of entanglement entropy at deconfined quantum criticality
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition
• Identifying the maximum entropy method as a special limit of stochastic analytic continuation
• Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2+1 dimensions
• Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
• Entanglement Hamiltonians of lattice models via the Bisognano-Wichmann theorem
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Realization of Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model
• Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions
• Entanglement Hamiltonian of Interacting Fermionic Models
• Dynamics of Topological Excitations in a Model Quantum Spin Ice
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
• Dynamical structure factors and excitation modes of the bilayer Heisenberg model
• Entanglement entropy from nonequilibrium work
• Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions
• Sweeping cluster algorithm for quantum spin systems with strong geometric restrictions
• Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo
• Scaling of disorder operator at deconfined quantum criticality
• Dynamical Signature of Symmetry Fractionalization in Frustrated Magnets
• Triangular lattice quantum dimer model with variable dimer density
• Universal Features of Higher-Form Symmetries at Phase Transitions
• Shannon-Rényi entropies and participation spectra across 3d $O(3)$ criticality
• Higher-form symmetry breaking at Ising transitions
• A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations
• Entanglement at a Two-Dimensional Quantum Critical Point: a T=0 Projector Quantum Monte Carlo Study
• Scaling of disorder operator at $(2+1)d$ U(1) quantum criticality
• Reconstructing Entanglement Hamiltonian via Entanglement Eigenstates
• Topological phase transition and single/multi anyon dynamics of $Z_2$ spin liquid
• Exciton Proliferation and Fate of the Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model
• Entanglement Hamiltonian of quantum critical chains and conformal field theories
• Dynamical properties of collective excitations in twisted bilayer Graphene
• Amplitude Mode in Quantum Magnets via Dimensional Crossover
• Entanglement Spectroscopy using Quantum Monte Carlo
• Entanglement Entropy of Non-Hermitian Free Fermions
• Topological Disorder Parameter
• Quantum dynamics of topological strings in a frustrated Ising antiferromagnet
• Categorical Symmetries at Criticality
• Fractionalized conductivity and emergent self-duality near topological phase transitions
• Entanglement-spectrum characterization of ground-state nonanalyticities in coupled excitation-phonon models
• Fermion sign bounds theory in quantum Monte Carlo simulation
• Monte Carlo study of the pseudogap and superconductivity emerging from quantum magnetic fluctuations
• Vestigial anyon condensation in kagome quantum spin liquids
• Entanglement Hamiltonian of Many-body Dynamics in Strongly-correlated Systems
• Bulk and edge dynamics of a 2D Affleck-Kennedy-Lieb-Tasaki model
• Entanglement spectrum of geometric states
• Emergent Rokhsar-Kivelson point in realistic quantum Ising models
• Critical Scaling Behaviors of Entanglement Spectra

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• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Universal entanglement spectrum in gapless symmetry protected topological states
• Stable computation of entanglement entropy for 2D interacting fermion systems
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• Evolution from quantum anomalous Hall insulator to heavy-fermion semimetal in magic-angle twisted bilayer graphene
• An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation
• Different temperature-dependence for the edge and bulk of entanglement Hamiltonian
• Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian
• Demonstrating the wormhole mechanism of the entanglement spectrum via a perturbed boundary
• Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders
• Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
• Universal Behavior in Entanglement Entropy Reveals Quantum Criticality and Underlying Symmetry Breaking
• Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum
• Accessing Excitation of Many-body Systems via Single-Mode Approximation within Quantum Monte Carlo Simulations
• Spectral Projections for Density Matrices in Quantum Field Theories
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study
• Boundary Renormalization Group Flow of Entanglement Entropy at a (2+1)-Dimensional Quantum Critical Point