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Abstract
Results about entanglement (or modular) Hamiltonians of quantum manybody 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 nonintegrable 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 manybody systems are summarized. These include protocols to measure entanglement spectra, and schemes to perform state tomography.
Original language  English 

Article number  2200064 
Journal  Annalen der Physik 
Early online date  17 Aug 2022 
DOIs  
Publication status  Epub ahead of print  17 Aug 2022 
Keywords
 entanglement
 quantum field theory
 quantum simulation
 strongly correlated systems
ASJC Scopus subject areas
 Physics and Astronomy(all)
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 1 Active

FWF  Entanglement  Entanglement Hamiltonians in quantum manybody physics
16/12/21 → 30/04/25
Project: Research project