Entanglement and Conservation Laws in Many-Body Systems

How are symmetries, which give rise to conservation laws, manifested by entanglement measures? Similarly to the system Hamiltonian, a subsystem's reduced density matrix is composed of blocks characterized by symmetry quantum numbers, or charge sectors. I will present a geometric method for extracting the contribution of individual charge sectors to a subsystem’s entanglement measures within the replica approach, via threading of appropriate conjugate Aharonov-Bohm fluxes through a multi-sheeted Riemann surface.
Specializing to the case of 1+1D conformal field theory, I will describe a general exact result for the entanglement characteristics. I will apply it to a variety of systems, ranging from free and interacting fermions to spin and parafermion chains, and verify it numerically. For example, I will show that the total entanglement entropy, which scales as the logarithm of the subsystem size, is composed of square-root of log contributions of individual subsystem charge sectors for interacting fermion chains, or even subsystem-size-independent contributions when total spin conservation is also accounted for. I will also describe how measurements of the contribution to the entanglement from separate charge sectors can be performed in ultracold atoms and similar systems.