Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system

Abstract

Beyond the Li-Haldane-Poilblanc conjecture, we find the entanglement Hamiltonian (EH) is actually not closely similar to the original Hamiltonian on the virtual edge. Unexpectedly, the EH has some relevant long-range interacting terms which hugely affect the physics. Without loss of generality, we study a spin-1/2 Heisenberg bilayer to obtain the entanglement information between the two layers through our newly developed quantum Monte Carlo scheme, which can simulate large-scale EH. Although the entanglement spectrum carrying the Goldstone mode seems like a Heisenberg model on a single layer, which is consistent with Li-Haldane-Poilblanc conjecture, we demonstrate that there actually exists a finite-temperature phase transition of the EH. The results violate the Mermin-Wagner theorem, which means there should be relevant long-range terms in the EH. It reveals that the Li-Haldane-Poilblanc conjecture ignores necessary corrections for the EH which may lead totally different physics.

arXiv comment9 pages, 4 figures

References in corpus (84)

• 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
• Stochastic series expansion method with operator-loop update
• Computational Studies of Quantum Spin Systems
• 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
• Entanglement hamiltonians in two-dimensional conformal field theory
• 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
• Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
• 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
• Entanglement spectra of quantum Heisenberg ladders
• Quantum Simulation and Spectroscopy of Entanglement Hamiltonians
• Universal behavior beyond multifractality in quantum many-body systems
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Quantum Entanglement of Interacting Fermions in Monte Carlo
• Measurement Protocol for the Entanglement Spectrum of Cold Atoms
• How universal is the entanglement spectrum?
• Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions
• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Scaling of entanglement entropy at deconfined quantum criticality
• Entanglement spectrum of the two dimensional Bose-Hubbard model
• Exploring Large-Scale Entanglement in Quantum Simulation
• 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
• Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
• Entanglement Spectrum Classification of $C_n$-invariant Noninteracting Topological Insulators in Two Dimensions
• Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions
• Entanglement Hamiltonian of Interacting Fermionic Models
• Entanglement spectra of coupled S=1/2 spin chains in a ladder geometry
• 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 Hamiltonians: from field theory, to lattice models and experiments
• Metastability and discrete spectrum of long-range systems
• Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions
• Sweeping cluster algorithm for quantum spin systems with strong geometric restrictions
• Scaling of disorder operator at deconfined quantum criticality
• Universal Features of Higher-Form Symmetries at Phase Transitions
• Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases
• Shannon-Rényi entropies and participation spectra across 3d $O(3)$ criticality
• Upper and Lower Critical Decay Exponents of Ising Ferromagnets with Long-range Interaction
• Spin Waves in Antiferromagnetic Spin Chains with Long Range Interactions
• On the continuum limit of the entanglement Hamiltonian
• Reconstructing Entanglement Hamiltonian via Entanglement Eigenstates
• Entanglement Hamiltonians for non-critical quantum chains
• Global scheme of sweeping cluster algorithm to sample among topological sectors
• Amplitude Mode in Quantum Magnets via Dimensional Crossover
• Entanglement Spectroscopy using Quantum Monte Carlo
• Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
• Categorical Symmetries at Criticality
• Unlocking the general relationship between energy and entanglement spectra via the wormhole effect
• Generalized Higgs mechanism in long-range interacting quantum systems
• Characterizing Topological Excitations of a Long-Range Heisenberg Model with Trapped Ions
• Critical entanglement spectrum of one-dimensional symmetry protected topological phases
• Measuring von Neumann entanglement entropies without wave functions
• Entanglement-spectrum characterization of ground-state nonanalyticities in coupled excitation-phonon models
• Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model
• On the continuum limit of the entanglement Hamiltonian of a sphere for the free massless scalar field
• Entanglement Hamiltonian of Many-body Dynamics in Strongly-correlated Systems
• Dynamical properties of quantum many-body systems with long range interactions
• Bulk and edge dynamics of a 2D Affleck-Kennedy-Lieb-Tasaki model
• Classical model emerges in quantum entanglement: Quantum Monte Carlo study for an Ising-Heisenberg bilayer
• Entanglement spectrum of geometric states
• Different temperature-dependence for the edge and bulk of entanglement Hamiltonian
• Demonstrating the wormhole mechanism of the entanglement spectrum via a perturbed boundary
• Entanglement conductance as a characterization of delocalized-localized phase transition in free fermion models
• Critical Scaling Behaviors of Entanglement Spectra
• Entanglement spectrum of fermionic bilayer honeycomb lattice: Hofstadter butterfly
• Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders
• Intercomponent entanglement entropy and spectrum in binary Bose-Einstein condensates

Cited by in corpus (4)

• Universal entanglement spectrum in gapless symmetry protected topological states
• Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures
• Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study