“Entanglement Entropy in Many-Body Systems: Disorder and Symmetry”

Dr. Moshe Goldstein
School of Physics and Astronomy, Tel Aviv University

Jun. 19 (Tue.), 11:00 AM
E6-2. 2nd fl. #2502

Abstract:
Entanglement has recently emerged as a central theme in the study of many-body systems. In this talk I will discuss two novel aspects of this subject.
The first is the use of entanglement to characterize disordered topological phases, in particular the Kitaev chain. I will show that surprisingly, disorder may help induce entanglement and even topological behavior in these systems.
The second has to do with systems with symmetries, which give rise to conservation laws. 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 approach for extracting the contribution of individual charge sectors to a subsystem’s entanglement measures within the replica trick method, 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 then apply this result 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 with existing techniques.