Classical model emerges in quantum entanglement: Quantum Monte Carlo study for an Ising-Heisenberg bilayer

Abstract

By developing a cluster sampling of stochastic series expansion quantum Monte Carlo method, we investigate a spin-$1/2$ model on a bilayer square lattice with intra-layer ferromagnetic (FM) Ising coupling and inter-layer antiferromagnetic Heisenberg interaction. The continuous quantum phase transition which occurs at $g_c=3.045(2)$ between the FM Ising phase and the dimerized phase is studied via large scale simulations. From the analyzes of critical exponents we show that this phase transition belongs to the (2+1)-dimensional Ising universality class. Besides, the quantum entanglement is strong between the two layers, especially in dimerized phase. The effective Hamiltonian of single layer seems like a transverse field Ising model. However, we found the quantum entanglement Hamiltonian is a pure classical Ising model without any quantum fluctuations. Furthermore, we give a more general explanation about how a classical entanglement Hamiltonian emerges.

References in corpus (28)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Continuum Model of the Twisted Bilayer
• Entanglement spectrum in one-dimensional systems
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Numerical studies of confined states in rotated bilayers of graphene
• Universal terms for the entanglement entropy in 2+1 dimensions
• Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
• Entanglement Hamiltonian Tomography in Quantum Simulation
• Scaling of entanglement entropy at deconfined quantum criticality
• Realization of Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
• Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions
• Scaling of disorder operator at deconfined quantum criticality
• Universal Features of Higher-Form Symmetries at Phase Transitions
• Global scheme of sweeping cluster algorithm to sample among topological sectors
• Dynamical properties of collective excitations in twisted bilayer Graphene
• Superconductivity and bosonic fluid emerging from Moiré flat bands
• Quantum dynamics of topological strings in a frustrated Ising antiferromagnet
• Categorical Symmetries at Criticality
• Vestigial anyon condensation in kagome quantum spin liquids
• Ground state phase diagram of the half-filled bilayer Hubbard model
• Entanglement spectrum of geometric states
• Quantum tricriticality of incommensurate phase induced by quantum domain walls in frustrated Ising magnetism

Cited by in corpus (7)

• Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian
• Different temperature-dependence for the edge and bulk of entanglement Hamiltonian
• Demonstrating the wormhole mechanism of the entanglement spectrum via a perturbed boundary
• 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
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study