Entanglement Hamiltonians: From Field Theory to Lattice Models and Experiments

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 Ha...

Full description

Saved in:
Bibliographic Details
Published in:Annalen der Physik 2022-11, Vol.534 (11), p.n/a
Main Authors: Dalmonte, Marcello, Eisler, Viktor, Falconi, Marco, Vermersch, Benoît
Format: Article
Language:English
Subjects:
Data processing
entanglement
Hamiltonian functions
Quantum entanglement
Quantum field theory
Quantum phenomena
quantum simulation
Quantum theory
Statistical mechanics
strongly correlated systems
Theorems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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. Entanglement is a genuine form of quantum correlation, which plays a pivotal role in characterizing collective phenomena, from topological order to criticality and beyond. Here, results about entanglement Hamiltonians—an operator‐based characterization of entanglement—in many‐body systems are reviewed, from field theory and statistical mechanics models, to recent applications in the context of quantum information and quantum simulation.
ISSN:0003-3804
1521-3889
DOI:10.1002/andp.202200064