Student Seminar | June 30, 16:30
Modular operator, correlation functions and symmetry resolution
In quantum mechanical systems, the reduced density matrix and the associated entanglement Hamiltonian provide a characterization of the entanglement structure of a state. In the presence of symmetries, quantities such as the entanglement entropy can be decomposed into subregion charge sectors, a program known as symmetry resolution. However, the definition of the reduced density matrix as well as the entanglement Hamiltonian rely on the spatial factorization of the Hilbert space, a property not present in quantum field theories. We study the modular operator, the natural analogue of the reduced density matrix in quantum field theory, and develop its decomposition into subregion charge sectors. This allows us to obtain the symmetry-resolved modular operator, modular flow, and modular correlation functions in the setting of hyperfinite von Neumann algebras. Our approach provides a mathematical foundation for recent results on symmetry resolution and modular theory in conformal field theory.
Würzburg U
0.03
Contact: Konstantin Weisenberger