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Thermalization is a ubiquitous process of statistical physics, in which details of few-body observables are washed out in favor of a featureless steady state. Even in isolated quantum many-body systems, limited to reversible dynamics, thermalization typically prevails. However, in these systems, there is another possibility: many-body localization (MBL) can result in preservation of a non-thermal state. While disorder has long been considered an essential ingredient for this phenomenon, recent theoretical work has suggested that a quantum many-body system with a uniformly increasing field -- but no disorder -- can also exhibit MBL, resulting in `Stark MBL. Here we realize Stark MBL in a trapped-ion quantum simulator and demonstrate its key properties: halting of thermalization and slow propagation of correlations. Tailoring the interactions between ionic spins in an effective field gradient, we directly observe their microscopic equilibration for a variety of initial states, and we apply single-site control to measure correlations between separate regions of the spin chain. Further, by engineering a varying gradient, we create a disorder-free system with coexisting long-lived thermalized and nonthermal regions. The results demonstrate the unexpected generality of MBL, with implications about the fundamental requirements for thermalization and with potential uses in engineering long-lived non-equilibrium quantum matter.
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We study the dynamics of an interacting quantum spin chain under the application of a linearly increasing field. This model exhibits a type of localization known as Stark many-body localization. The dynamics shows a strong dependence on the initial conditions, indicating that the system violates the conventional (strong) eigenstate thermalization hypothesis at any finite gradient of the field. This is contrary to reports of a numerically observed ergodic phase. Therefore, the localization is crucially distinct from disorder-driven many-body localization, in agreement with recent predictions on the basis of localization via Hilbert-space shattering.
Recent numerical and experimental works have revealed a disorder-free many-body localization (MBL) in an interacting system subjecting to a linear potential, known as the Stark MBL. The conventional MBL, induced by disorder, has been widely studied by using quantum simulations based on superconducting circuits. Here, we consider the Stark MBL in two types of superconducting circuits, i.e., the 1D array of superconducting qubits, and the circuit where non-local interactions between qubits are mediated by a resonator bus. We calculate the entanglement entropy and participate entropy of the highly-excited eigenstates, and obtain the lower bound of the critical linear potential $gamma_{c}$, using the finite-size scaling collapse. Moreover, we study the non-equilibrium properties of the Stark MBL. In particular, we observe an anomalous relaxation of the imbalance, dominated by the power-law decay $t^{-xi}$. The exponent $xi$ satisfies $xipropto|gamma-gamma_{c}|^{ u}$ when $gamma<gamma_{c}$, and vanishes for $gammageq gamma_{c}$, which can be employed to estimate the $gamma_{c}$. Our work indicates that superconducting circuits are a promising platform for investigating the critical properties of the Stark MBL transition.
Motivated by the question of whether disorder is a prerequisite for localization to occur in quantum many-body systems, we study a frustrated one-dimensional spin chain, which supports localized many-body eigenstates in the absence of disorder. When the system is prepared in an initial state with one domain wall, it exhibits characteristic signatures of quasi-many-body localization (quasi- MBL), including initial state memory retention, an exponentially increasing lifetime with enlarging the size of the system, a logarithmic growth of entanglement entropy, and a logarithmic light cone of an out-of-time-ordered correlator. We further show that the localized many-body eigenstates can be manipulated as pseudospin-1/2s and thus could potentially serve as qubits. Our findings suggest a new route of using frustration to access quasi-MBL and preserve quantum coherence.
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.
The Bloch oscillation (BO) and Wannier-Stark localization (WSL) are fundamental concepts about metal-insulator transitions in condensed matter physics. These phenomena have also been observed in semiconductor superlattices and simulated in platforms such as photonic waveguide arrays and cold atoms. Here, we report experimental investigation of BOs and WSL simulated with a 5-qubit programmable superconducting processor, of which the effective Hamiltonian is an isotropic $XY$ spin chain. When applying a linear potential to the system by properly tuning all individual qubits, we observe that the propagation of a single spin on the chain is suppressed. It tends to oscillate near the neighborhood of their initial positions, which demonstrates the characteristics of BOs and WSL. We verify that the WSL length is inversely correlated to the potential gradient. Benefiting from the precise single-shot simultaneous readout of all qubits in our experiments, we can also investigate the thermal transport, which requires the joint measurement of more than one qubits. The experimental results show that, as an essential characteristic for BOs and WSL, the thermal transport is also blocked under a linear potential. Our experiment would be scalable to more superconducting qubits for simulating various of out-of-equilibrium problems in quantum many-body systems.
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