Localization transition induced by programmable disorder

We investigate the occurrence of many-body localization (MBL) on a spin-1/2 transverse-field Ising model defined on a Chimera connectivity graph with random exchange interactions and longitudinal fields. We observe a transition from an ergodic phase to a nonthermal phase for individual energy eigenstates induced by a critical disorder strength for the Ising parameters. Our result follows from the analysis of both the mean half-system block entanglement and the energy-level statistics. We identify the critical point associated with this transition using the maximum variance of the block entanglement over the disorder ensemble as a function of the disorder strength. The calculated energy density phase diagram shows the existence of a mobility edge in the energy spectrum. In terms of the energy-level statistics, the system changes from the Gaussian orthogonal ensemble for weak disorder to a Poisson distribution limit for strong randomness, which implies localization behavior. We then realize the time-independent disordered Ising Hamiltonian experimentally using a reverse annealing quenchpause-quench protocol on a D-wave 2000Q programmable quantum annealer. We characterize the transition from the thermal to the localized phase through magnetization measurements at the end of the annealing dynamics, and the results are compatible with our theoretical prediction for the critical point. However, the same behavior can be reproduced using a classical spin-vector Monte Carlo simulation, which suggests that genuine quantum signatures of the phase transition remain out of reach using this experimental platform and protocol.