Symmetry-resolved Entanglement in Topological Insulators and Many-body Localized Phases

In a many-body system, entanglement is typically only partially extractable and transferable to a quantum register. The fundamental idea is that in order to extract it, a measurement of the local particle numner is required. Thus, the total entanglement S can be broken down into two symmetry-resolved components: the configurational (extractable) entropy S_C and number (easily measurable) entropy S_N. In the first part of my talk, I will show that in a C₂-symmetric topological systems, lower bounds for both quantities in terms of a topological invariant can be proven.

In the second part of my talk, I will consider the number entropy as a witness for particle transport following a quantum quench. For Gaussian systems, one can show that S_N(t)~ln S(t). I will show numerical results indicating that this relation also seems to hold in the interacting t-V chain with potential disorder (equivalent to the Heisenberg chain with random fields) in a phase which was previously assumed to be many-body localized. In particular, we find that S_N(t) ~ lnln(t) for all disorder strengths which are numerically accessible, indicating an ongoing transport of particles and the absence of localization. At a minimum, these results show that all previous estimates for the critical point separating the ergodic from a putative many-body localized phase have been incorrect.