Entanglement Hamiltonian of Interacting Systems: Local Temperature Approximation and Beyond

Abstract

We investigate the second quantization form of the entanglement Hamiltonian (EH) of various subregions for the ground-state of several interacting lattice fermions and spin models. The relation between the EH and the model Hamiltonian itself is an unsolved problem for the ground-state of generic local Hamiltonians. In this letter, we demonstrate that the EH is practically local and its dominant components are related to the terms present in the model Hamiltonian up to a smooth spatially varying temperature even for (a) discrete lattice systems, (b) systems with no emergent conformal or Lorentz symmetry, and (c) for subsystems with non-flat boundaries, up to relatively strong interactions. We show that the mentioned local temperature at a given point decays inversely proportional to its distance from the boundary between the subsystem and the environment. We find the subdominant terms in the EH as well and show that they are severely suppressed away from the boundaries of subsystem and are relatively small near them.

References in corpus (10)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Towards a derivation of holographic entanglement entropy
• Theory of Intertwined Orders in High Temperature Superconductors
• Entanglement hamiltonians in two-dimensional conformal field theory
• Entropy on a null surface for interacting quantum field theories and the Bousso bound
• Local temperatures and local terms in modular Hamiltonians
• On the continuum limit of the entanglement Hamiltonian
• Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains
• Reconstructing quantum states from local data
• Engineering Quantum Hall Phases in Synthetic Bilayer Graphene System