Different temperature-dependence for the edge and bulk of entanglement Hamiltonian

Abstract

We propose a physical picture based on the wormhole effect of the path-integral formulation to explain the mechanism of entanglement spectrum (ES), such that, our picture not only explains the topological state with bulk-edge correspondence of the energy spectrum and ES (the Li and Haldane conjecture), but is generically applicable to other systems independent of their topological properties. We point out it is ultimately the relative strength of bulk energy gap (multiplied with inverse temperature $\beta =1/T$) with respect to the edge energy gap that determines the behavior of the low-lying ES of the system. Depending on the circumstances, the ES can resemble the energy spectrum of the virtual edge, but can also represent that of the virtual bulk. We design models both in 1D and 2D to successfully demonstrate the bulk-like low-lying ES at finite temperatures, in addition to the edge-like case conjectured by Li and Haldane at zero temperature. Our results support the generality of viewing the ES as the wormhole effect in the path integral and the different temperature-dependence for the edge and bulk of ES.

5 pages, 3 figures

References in corpus (19)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Quantum Noise as an Entanglement Meter
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Entanglement from Charge Statistics: Exact Relations for Many-Body Systems
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1
• Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo
• A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations
• Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities
• Topological Disorder Parameter
• Unlocking the general relationship between energy and entanglement spectra via the wormhole effect
• Fermion sign bounds theory in quantum Monte Carlo simulation
• Evolution of Dynamical Signature in the X-cube Fracton Topological Order
• Classical model emerges in quantum entanglement: Quantum Monte Carlo study for an Ising-Heisenberg bilayer
• A Sport and a Pastime: Model Design and Computation in Quantum Many-Body Systems
• Critical Scaling Behaviors of Entanglement Spectra

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