On the Bisognano-Wichmann entanglement Hamiltonian of nonrelativistic fermions

TL;DR

This paper derives an exact form of the entanglement Hamiltonian for nonrelativistic fermions in one dimension, showing it matches the Bisognano-Wichmann form with a nonuniversal factor, applicable to both continuum and lattice models.

Contribution

It demonstrates that the Bisognano-Wichmann form of the entanglement Hamiltonian is exact for nonrelativistic fermions, extending previous relativistic results to nonrelativistic systems.

Findings

Exact eigenfunctions are superpositions of occupied modes weighted by inverse energy.

The entanglement Hamiltonian matches the Bisognano-Wichmann form up to a nonuniversal factor.

Results hold for both continuum and lattice models.

Abstract

We study the ground-state entanglement Hamiltonian of free nonrelativistic fermions for semi-infinite domains in one dimension. This is encoded in the two-point correlations projected onto the subsystem, an operator that commutes with the linear deformation of the physical Hamiltonian. The corresponding eigenfunctions are shown to possess the exact same structure both in the continuum as well as on the lattice. Namely, they are superpositions of the occupied single-particle modes of the total Hamiltonian, weighted by the inverse of their energy as measured from the Fermi level, and multiplied by an extra phase proportional to the integrated weight. Using this ansatz, we prove that the Bisognano-Wichmann form of the entanglement Hamiltonian becomes exact, up to a nonuniversal prefactor that depends on the dispersion for gapped chains.