Entanglement Hamiltonian of interacting systems: Local temperature approximation and beyond

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 paper, 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) subsystems with nonflat boundaries, up to relatively strong interactions. We show that the mentioned local temperature at a given point decays in a manner 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.

Automated summary

This study demonstrates that the entanglement Hamiltonian (EH) is practically local and its main components are related to the terms present in the model Hamiltonian, even for subsystems with non-flat boundaries and under strong interactions. The local temperature at a given point decays inversely proportional to its distance from the boundary between the subsystem and the environment, and the subdominant terms in the EH are severely suppressed away from the boundaries of the subsystem and relatively small near them.