Quantum Phase Transitions in the Disordered Ising Model

Abstract

The many-body localization phase transition in disordered systems has recently garnered much attention, as it has been shown to persist up to nonzero temperatures. We study this phase transition in the in nite temperature limit, and propose the existence of an eigenstate symmetry breaking phase transition within the localized phase. Through exact diagonalization calculations, we obtain evidence for the separate existence of both phase transitions as one tunes the strength of the disorder. This implies the existence of a localized spin glass phase in addition to the localized and thermal paramagnetic phases of the model. The renormalization group as applied to disordered systems is also used to show the existence of the broken symmetry phase, and we obtain data characterizing the symmetry breaking phase transition near its critical point.