Entanglement Hamiltonians: From Field Theory to Lattice Models and Experiments

Marcello Dalmonte*, Viktor Eisler, Marco Falconi, Benoit Vermersch

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review


Results about entanglement (or modular) Hamiltonians of quantum many-body systems in field theory and statistical mechanics models, and recent applications in the context of quantum information and quantum simulation, are reviewed. In the first part of the review, what is known about entanglement Hamiltonians of ground states (vacua) in quantum field theory is summarized, based on the Bisognano–Wichmann theorem and its extension to conformal field theory. This is complemented with a more rigorous mathematical discussion of the Bisognano–Wichmann theorem, within the framework of Tomita–Takesaki theorem of modular groups. The second part of the review is devoted to lattice models. There, exactly soluble cases are first considered and then the discussion is extended to non-integrable models, whose entanglement Hamiltonian is often well captured by the lattice version of the Bisognano–Wichmann theorem. In the last part of the review, recently developed applications in quantum information processing that rely upon the specific properties of entanglement Hamiltonians in many-body systems are summarized. These include protocols to measure entanglement spectra, and schemes to perform state tomography.

Original languageEnglish
Article number2200064
JournalAnnalen der Physik
Issue number11
Early online date17 Aug 2022
Publication statusPublished - Nov 2022


  • entanglement
  • quantum field theory
  • quantum simulation
  • strongly correlated systems

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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