Many-body localization near the critical point
MATHEMATICAL PICTURE LANGUAGE
John Imbrie - University of Virginia
I will examine the many-body localization (MBL) phase transition in one-dimensional quantum systems with quenched randomness. Having demonstrated the existence of the MBL phase at strong disorder, under a level-statistics assumption, I will focus on the nature of the transition out of this phase, using an approximate strong-disorder renormalization group. In this approach, the phase transition is due to the so-called avalanche instability of the MBL phase. I show that the critical behavior can be determined analytically within this RG. The RG flow near the critical fixed point is qualitatively similar to the Kosterlitz-Thouless (KT) flow, but there are important differences, and so this MBL transition is in a universality class that is distinct from KT. The divergence of the correlation length corresponds to critical exponent ν →∞, but the divergence is weaker than for the KT transition. This is joint work with Alan Morningstar and David Huse.