Abstract There are exceptions to the general observation that interacting quantum-many body systems thermalize. The most prominent case is many-body localization (MBL) where interactions drive localization in disordered lattice systems. In such systems, the eigenstate thermalization (ETH) hypothesis breaks down and the system remains in a non-thermal state. The existence of MBL in two-dimensional systems and the conditions on required disorder properties are still debated. Here, we study a two-dimensional fermionic quantum many-body system in Moiré-type quasiperiodic disorder and find a novel two-step transition to a MBL state. The intermediate state shows anisotropic transport induced by partial localization. Our work paves the way for the study of the numerous intriguing phenomena observed in Moiré lattice materials and our observations ask for further studies on localization in more complex Moiré structures.
Abstract There are exceptions to the general observation that interacting quantum-many body systems thermalize. The most prominent case is many-body localization (MBL) where interactions drive localization in disordered lattice systems. In such systems, the eigenstate thermalization (ETH) hypothesis breaks down and the system remains in a non-thermal state. The existence of MBL in two-dimensional systems and the conditions on required disorder properties are still debated. Here, we study a two-dimensional fermionic quantum many-body system in Moiré-type quasiperiodic disorder and find a novel two-step transition to a MBL state. The intermediate state shows anisotropic transport induced by partial localization. Our work paves the way for the study of the numerous intriguing phenomena observed in Moiré lattice materials and our observations ask for further studies on localization in more complex Moiré structures.
In a many-body localized (MBL) quantum system, the ergodic hypothesis breaks down, giving rise to a fundamentally new many-body phase. Whether and under which conditions MBL can occur in higher dimensions remains an outstanding challenge both for experiments and theory. Here, we experimentally explore the relaxation dynamics of an interacting gas of fermionic potassium atoms loaded in a two-dimensional optical lattice with different quasiperiodic potentials along the two directions. We observe a dramatic slowing down of the relaxation for intermediate disorder strengths. Furthermore, beyond a critical disorder strength, we see negligible relaxation on experimentally accessible time scales, indicating a possible transition into a two-dimensional MBL phase. Our experiments reveal a distinct interplay of interactions, disorder, and dimensionality and provide insights into regimes where controlled theoretical approaches are scarce.
We study localization driven solely by interparticle interactions in moiré lattice systems without intrinsic disorder or externally imposed quasiperiodic potentials. We consider a one-dimensional bilayer with incommensurate lattice constants, described by a spin-dependent Fermi-Hubbard-type model with short-range interlayer interactions, where quasiperiodicity emerges only through interactions. Exact diagonalization shows that quenching hopping in one layer generates an interaction-induced mosaic potential with multiple mobility edges. When both layers are dynamical, increasing interlayer interactions drives transitions among ergodic, critical, and many-body localized regimes, with energy-dependent coexistence in certain parameter ranges. An exact mapping to a noninteracting single-particle model on a higher-dimensional structured graph provides a unified interpretation of these results and suggests an experimentally accessible route to interaction-induced moiré physics and localization.
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.
Whether disordered and quasiperiodic many-body quantum systems host a long-lived localized phase in the thermodynamic limit has been the subject of intense recent debate. While in one dimension, substantial evidence for such a many-body localized (MBL) phase exists, the behavior in higher dimensions remains an open puzzle. In disordered systems, for instance, it has been argued that rare regions may lead to thermalization of the whole system through a mechanism dubbed avalanche instability. In quasiperiodic systems, however, rare regions are altogether absent and the fate of a putative many-body localized phase has hitherto remained largely unexplored. In this work, we investigate the localization properties of two many-body quasiperiodic models, which are two-dimensional generalizations of the Aubry-Andr\'e model. By studying numerically the out-of-equilibrium dynamics of large systems, we find very long-lived localization on experimentally relevant time scales. Surprisingly, we also observe large-scale transport along deterministic lines of weak potential, which appear in the investigated quasiperiodic models. Our results demonstrate that quasiperiodic many-body systems have the remarkable and counter-intuitive capability of exhibiting coexisting localization and transport properties---a phenomenon reminiscent of the behavior of supersolids. Our findings are of direct experimental relevance and can be tested, for instance, using state-of-the-art cold atomic systems.
Localization in one-dimensional interacting systems can be caused by disorder potentials or non-Hermiticity. The former phenomenon is the many-body localization (MBL), and the latter is the many-body non-Hermitian skin effect (NHSE). In this work, we numerically investigate the interplay between these two kinds of localization, where the energy-resolved MBL arises from a deterministic quasiperiodic potential in a fermionic chain. We propose a set of eigenstate properties and long-time dynamics that collectively distinguish the two localization mechanisms in the presence of non-Hermiticity. By computing the proposed diagnostics, we show that the thermal states are vulnerable to the many-body NHSE while the MBL states remain resilient up to a strong non-Hermiticity. Finally, we discuss experimental observables that probe the difference between the two localizations in a non-Hermitian quasiperiodic fermionic chain. Our results pave the way toward experimental observations on the interplay of interaction, quasiperiodic potential, and non-Hermiticity.
Many-body localization (MBL) is currently a hot issue of interacting systems, in which quantum mechanics overcomes thermalization of statistical mechanics. Like Anderson localization of non-interacting electrons, disorders are usually crucial in engineering the quantum interference in MBL. For translation invariant systems, however, the breakdown of eigenstate thermalization hypothesis due to a pure many-body quantum effect is still unclear. Here we demonstrate a possible MBL phenomenon without disorder, which emerges in a lightly doped Hubbard model with very strong interaction. By means of density matrix renormalization group numerical calculation on a two-leg ladder, we show that whereas a single hole can induce a very heavy Nagaoka polaron, two or more holes will form bound pair/droplets which are all localized excitations with flat bands at low energy densities. Consequently, MBL eigenstates of finite energy density can be constructed as composed of these localized droplets spatially separated. We further identify the underlying mechanism for this MBL as due to a novel 'Berry phase' of the doped Mott insulator, and show that by turning off this Berry phase either by increasing the anisotropy of the model or by hand, an eigenstate transition from the MBL to a conventional quasiparticle phase can be realized.