On the Bisognano-Wichmann entanglement Hamiltonian of nonrelativistic fermions

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.

17 pages, 5 figures

References in corpus (11)

• Towards a derivation of holographic entanglement entropy
• Entanglement hamiltonians in two-dimensional conformal field theory
• The entanglement entropy of one-dimensional gases
• Exploring Large-Scale Entanglement in Quantum Simulation
• Local temperatures and local terms in modular Hamiltonians
• Entanglement Hamiltonians: from field theory, to lattice models and experiments
• On the continuum limit of the entanglement Hamiltonian
• Entanglement Hamiltonians for non-critical quantum chains
• Entanglement Hamiltonian in the non-Hermitian SSH model
• On the mass dependence of the modular operator for a double cone
• Entanglement Hamiltonian of a nonrelativistic Fermi gas