While many-body localization (MBL) is a well-established phenomenon in one-dimension, the fate of higher-dimensional strongly disordered systems in the infinite-time limit is a topic of current debate. The latest experiments as well as several recent numerical studies indicate that such systems behave many-body localized -- at least on practically relevant time scales. However, thus far, theoretical approaches have been unable to quantitatively reproduce experimentally measured MBL-to-thermal transition points, an important requirement to demonstrate their validity. Here, we develop a formalism to apply fermionic quantum circuits combined with automatic differentiation to simulate two-dimensional MBL systems realized in optical lattice experiments with fermions. Using entanglement-based features, we obtain a phase transition point in excellent agreement with the experimentally measured value. We argue that our approach best captures the underlying charge-density-wave experiments and calculate other quantities which can be compared to future experiments, such as the mean localization lengths.
Many-body localization (MBL), the disorder-induced localization of interacting particles, signals a breakdown of conventional thermodynamics because MBL systems do not thermalize and show nonergodic time evolution. We experimentally observed this nonergodic evolution for interacting fermions in a one-dimensional quasirandom optical lattice and identified the MBL transition through the relaxation dynamics of an initially prepared charge density wave. For sufficiently weak disorder, the time evolution appears ergodic and thermalizing, erasing all initial ordering, whereas above a critical disorder strength, a substantial portion of the initial ordering persists. The critical disorder value shows a distinctive dependence on the interaction strength, which is in agreement with numerical simulations. Our experiment paves the way to further detailed studies of MBL, such as in noncorrelated disorder or higher dimensions.
Many-body localization (MBL) is a dynamical phenomenon that describes the non-ergodicity of isolated quantum many-body systems. In contrast to thermalization, this phenomenon leads to a long-lived memory of initial states of local systems and slow growth of entanglement. In this work, we study Stark MBL in a 12-qubit correlated fermionic system described by the one-dimensional Fermi-Hubbard model using Hamiltonian simulation on an IBM superconducting qubit quantum computer. To enable such a computation on current-day noisy hardware, we combine a series of compilation steps, including the use of the spin-resolved Jordan-Wigner transformation, employing SWAP networks, and integrating a tensor-network-based quantum circuit optimization routine on top of a standard circuit optimization pipeline. As a result, there is approximately an 88
% and 87
% reduction in two-qubit gate count and circuit depth, respectively. Through such simulations of the real-time dynamics using Trotterized quantum circuits, we exhibit a crossover from thermalizing dynamics of the system at a weak tilt of the field to a strongly localized behavior at large tilt with short evolution times. We also benchmark our obtained results with respect to those from exact simulations.