Eigenstate phases with on-site finite non-Abelian symmetry

Abhishodh Prakash

Potter and Vasseur recently conjectured [1] that full many-body localization (MBL) is incompatible with finite non-Abelian symmetries unless it is spontaneously broken down to an Abelian subgroup. In this talk, I will present a numerical investigation of this conjecture by building a local spin Hamiltonian invariant under the action of the simplest non-Abelian group, S_3. Using full entanglement distributions and level statistics, we observe a thermal phase and an MBL phase where S_3 is spontaneously broken down to Z_3 resulting in a spin-glass like order in highly excited states. For a certain parameter range, there appears to be an intermediate region where full MBL is absent while S_3 is intact. I will speculate on the nature of this region. This talk is based on the results from our paper [2]

http://scgp.stonybrook.edu/video_portal/video.php?id=3320

Simons- Program: Hydrodynamics, ergodicity, entanglement and localization in interacting lattice models and field theories