At the Conference on “Complex Quantum Systems out of Equilibrium” in Murcia, Spain I presented my latest work with Dmitry Abanin on the relation between MBL and spin glasses. This work has been published on the arXiv now as well. The full presentation slides can be downloaded here (PDF).
Title: Unconventional Many-Body Localization in Long-Range Quantum Spin Glasses
Abstract: Spin glasses are a well-studied class of classical systems where random interactions lead to spin freezing at low temperatures. On the other hand, many-body localization is a quantum phe- nomenon where randomness and interactions lead to localization characterized by, amongst others, area law entanglement entropy and local integrals of motion. We show that a third, intermediate, state can emerge in a long-range one-dimensional spin glass under the applica- tion of a transverse field. At small applied fields and low temperatures the spin glass order remains, as characterized by the Edwards-Anderson order parameter. However, interacting low-energy spin resonances at large distances create unconventional long-range entanglement in eigenstates. The quench dynamics therefore display a wide variety in possible results: while some spins remain frozen, others ‘thaw’. The ”quantum spin glass” is therefore neither ergodic, nor many-body localized.
