Many Body Localization: A Macroscopic Quantum Phenomena in Highly Excited States
In 1958 P. W. Anderson showed that eigenstates of a single-particle quantum Hamiltonian in the presence of disorder can be localized in space. In the same paper he had speculated on the possibility of lack of thermalization in an isolated quantum system even in the presence of interactions.
There is now growing evidence that such an isolated system in the presence of strong disorder fails to equilibrate. This phenomena is being referred to as it many-body localization (MBL). I will introduce the various defining characteristics of the MBL phase and the measures which can be used to distinguish it from the ergodic phase. Based on these I will show some numerical evidence of the hypothesized phase-transition between the MBL and thermal phases in a short-ranged model.
I will also describe the many-body localization-delocalization (MBLD) transition in a mean-field quantum spin glass. Such a model opens the possibility of developing a mean-field theory of the critical point which is an open question. Due to the violation of ergodicity MBL allows the existence of symmetry-breaking and topological order even in highly excited eigenstates, which would normally be destroyed by thermal fluctuations. I will present a phenomenological description of this localization protected quantum order.