When a system thermalizes it loses all memory of its initial conditions. Even within a closed quantum system, subsystems usually thermalize using the rest of the system as a heat bath. Exceptions to quantum thermalization have been observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize despite strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. We experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium with respect to the Hamiltonian. Using experimental and numerical methods we observe the essential signatures of MBL: initial state memory retention, Poissonian distributed many-body energy level spacings, and evidence of long-time entanglement growth. Our platform can be scaled to more spins, where detailed modeling of MBL becomes impossible.
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 quench-pause-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.
The discrete time crystal (DTC) is a nonequilibrium phase of matter that spontaneously breaks time-translation symmetry. Disorder-induced many-body localization can stabilize the DTC phase by breaking ergodicity and preventing thermalization. Here, we observe the hallmark signatures of the many-body–localized DTC using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. We demonstrate long-lived period-doubled oscillations and confirm that they are robust for generic initial states, thus showing the characteristic time-crystalline order across the many-body spectrum. Our results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.