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Many-body localization (MBL) describes a quantum phase where an isolated interacting system subject to sufficient disorder displays non-ergodic behavior, evading thermal equilibrium that occurs under its own dynamics. Previously, the thermalization-MBL transition has been largely characterized with the growth of disorder. Here, we explore a new axis, reporting on an energy resolved MBL transition using a 19-qubit programmable superconducting processor, which enables precise control and flexibility of both disorder strength and initial state preparations. We observe that the onset of localization occurs at different disorder strengths, with distinguishable energy scales, by measuring time-evolved observables and many-body wavefunctions related quantities. Our results open avenues for the experimental exploration of many-body mobility edges in MBL systems, whose existence is widely debated due to system size finiteness, and where exact simulations in classical computers become unfeasible.
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We investigate the occurrence of the phenomenon of many-body localization (MBL) on a D-Wave 2000Q programmable quantum annealer. We study a spin-1/2 transverse-field Ising model defined on a Chimera connectivity graph, with random exchange interactions and random longitudinal fields. On this system we experimentally observe a transition from an ergodic phase to an MBL phase. We first theoretically show that the MBL transition is induced by a critical disorder strength for individual energy eigenstates in a Chimera cell, which follows from the analysis of the mean half-system block entanglement, as measured by the von Neumann entropy. We show the existence of an area law for the block entanglement over energy eigenstates for the MBL phase, which stands in contrast with an extensive volume scaling in the ergodic phase. The identification of the MBL critical point is performed via the measurement of the maximum variance of the mean block entanglement over the disorder ensemble as a function of the disorder strength. Our results for the energy density phase diagram also show the existence of a many-body mobility edge in the energy spectrum. The time-independent disordered Ising Hamiltonian is then experimentally realized by applying the reverse annealing technique allied with a pause-quench protocol on the D-Wave device. We then characterize the MBL critical point through magnetization measurements at the end of the annealing dynamics, obtaining results compatible with our theoretical predictions for the MBL transition.
Quantum emulators, owing to their large degree of tunability and control, allow the observation of fine aspects of closed quantum many-body systems, as either the regime where thermalization takes place or when it is halted by the presence of disorder. The latter, dubbed many-body localization (MBL) phenomenon, describes the non-ergodic behavior that is dynamically identified by the preservation of local information and slow entanglement growth. Here, we provide a precise observation of this same phenomenology in the case the onsite energy landscape is not disordered, but rather linearly varied, emulating the Stark MBL. To this end, we construct a quantum device composed of thirty-two superconducting qubits, faithfully reproducing the relaxation dynamics of a non-integrable spin model. Our results describe the real-time evolution at sizes that surpass what is currently attainable by exact simulations in classical computers, signaling the onset of quantum advantage, thus bridging the way for quantum computation as a resource for solving out-of-equilibrium many-body problems.
Characterizing states of matter through the lens of their ergodic properties is a fascinating new direction of research. In the quantum realm, the many-body localization (MBL) was proposed to be the paradigmatic ergodicity breaking phenomenon, which extends the concept of Anderson localization to interacting systems. At the same time, random matrix theory has established a powerful framework for characterizing the onset of quantum chaos and ergodicity (or the absence thereof) in quantum many-body systems. Here we numerically study the spectral statistics of disordered interacting spin chains, which represent prototype models expected to exhibit MBL. We study the ergodicity indicator $g=log_{10}(t_{rm H}/t_{rm Th})$, which is defined through the ratio of two characteristic many-body time scales, the Thouless time $t_{rm Th}$ and the Heisenberg time $t_{rm H}$, and hence resembles the logarithm of the dimensionless conductance introduced in the context of Anderson localization. We argue that the ergodicity breaking transition in interacting spin chains occurs when both time scales are of the same order, $t_{rm Th} approx t_{rm H}$, and $g$ becomes a system-size independent constant. Hence, the ergodicity breaking transition in many-body systems carries certain analogies with the Anderson localization transition. Intriguingly, using a Berezinskii-Kosterlitz-Thouless correlation length we observe a scaling solution of $g$ across the transition, which allows for detection of the crossing point in finite systems. We discuss the observation that scaled results in finite systems by increasing the system size exhibit a flow towards the quantum chaotic regime.
We show that the magnetization of a single `qubit spin weakly coupled to an otherwise isolated disordered spin chain exhibits periodic revivals in the localized regime, and retains an imprint of its initial magnetization at infinite time. We demonstrate that the revival rate is strongly suppressed upon adding interactions after a time scale corresponding to the onset of the dephasing that distinguishes many-body localized phases from Anderson insulators. In contrast, the ergodic phase acts as a bath for the qubit, with no revivals visible on the time scales studied. The suppression of quantum revivals of local observables provides a quantitative, experimentally observable alternative to entanglement growth as a measure of the `non-ergodic but dephasing nature of many-body localized systems.
In the presence of sufficiently strong disorder or quasiperiodic fields, an interacting many-body system can fail to thermalize and become many-body localized. The associated transition is of particular interest, since it occurs not only in the ground state but over an extended range of energy densities. So far, theoretical studies of the transition have focused mainly on the case of true-random disorder. In this work, we experimentally and numerically investigate the regime close to the many-body localization transition in quasiperiodic systems. We find slow relaxation of the density imbalance close to the transition, strikingly similar to the behavior near the transition in true-random systems. This dynamics is found to continuously slow down upon approaching the transition and allows for an estimate of the transition point. We discuss possible microscopic origins of these slow dynamics.
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