We study the effect of spatially correlated classical noise on both Anderson and many-body localization of a disordered fermionic chain. By analyzing the evolution of the particle density imbalance following a quench from an initial charge density wave state, we find prominent signatures of localization also in the presence of the time-dependent noise, even though the system eventually relaxes to the infinite temperature state. In particular, for sufficiently strong static disorder, we observe the onset of metastability, which becomes more prominent the stronger the spatial correlations of the noise. In this regime, we find that the imbalance decays as a stretched-exponential---a behavior characteristic of glassy systems. We identify a simple scaling behavior of the relevant relaxation times in terms of the static disorder and of the noise correlation length. We discuss how our results could be exploited to extract information about the localization length in experimental setups.
We study the effect of spatially correlated classical noise on both Anderson and many-body localization of a disordered fermionic chain. By analyzing the evolution of the particle density imbalance following a quench from an initial charge density wave state, we find prominent signatures of localization also in the presence of the time-dependent noise, even though the system eventually relaxes to the infinite temperature state. In particular, for sufficiently strong static disorder, we observe the onset of metastability, which becomes more prominent the stronger the spatial correlations of the noise. In this regime, we find that the imbalance decays as a stretched-exponential---a behavior characteristic of glassy systems. We identify a simple scaling behavior of the relevant relaxation times in terms of the static disorder and of the noise correlation length. We discuss how our results could be exploited to extract information about the localization length in experimental setups.
We investigate the non-equilibrium dynamics of the disordered one-dimensional Fermi-Hubbard model with a focus on many-body localization. The system is initialized in a charge-density-wave-state, and its time evolution is analyzed through sublattice imbalance (spin and charge), and bipartite entanglement entropy. A clear crossover from ergodic to non-ergodic behavior is observed with increasing disorder strength. In the weak disorder regime, rapid decay of imbalance and the fast growth of entanglement indicate efficient thermalization. In contrast, a strong disorder leads to persistent imbalance and slow dynamics, signaling the breakdown of ergodicity. The charge and spin sectors exhibit distinct relaxation behavior, providing evidence for partial decoupling between these degrees of freedom. Furthermore, in the interacting regime, the entanglement entropy shows slow logarithmic growth, reflecting the dephasing-driven dynamics characteristic of the many-body localized phase. These results highlight the interplay between disorder and interactions in determining the dynamical properties of the system and establish robust signatures of many-body localization in the Fermi-Hubbard model.
We study the nonequilibrium evolution of a one-dimensional quantum Ising chain with spatially disordered, time-dependent, transverse fields characterized by white noise correlation dynamics. We establish prethermalization in this model, showing that the quench dynamics of the on-site transverse magnetization first approaches a metastable state unaffected by noise fluctuations, and then relaxes exponentially fast toward an infinite temperature state as a result of the noise. We also consider energy transport in the model, starting from an inhomogeneous state with two domain walls which separate regions characterized by spins with opposite transverse magnetization. We observe at intermediate timescales a phenomenology akin to Anderson localization: energy remains localized within the two domain walls, until the Markovian noise destroys coherence and, accordingly, disorder-induced localization, allowing the system to relax toward the late stages of its nonequilibrium dynamics. We compare our results with the simpler case of a noisy quantum Ising chain without disorder, and we find that the prethermal plateau is a generic property of spin chains with weak noise, while the phenomenon of prethermal Anderson localization is a specific feature arising from the competition of noise and disorder in the real-time transport properties of the system.
We study the dynamics of one- and two-dimensional disordered lattice bosons/fermions initialized to a Fock state with 1 particle on a set of lattice sites (A) and 0 particles on the rest of the sites (A). Such states have been considered in recent ultracold atomic experiments to detect many body localization. For noninteracting systems we establish a universal relation between the long time density imbalance between A and A sites, $I(\ensuremath{\infty})$, the localization length ${\ensuremath{\xi}}_{l}$, and the geometry of the initial pattern. For the alternating initial pattern of 1 and 0 particles in one dimension, $I(\ensuremath{\infty})=tanh[a/{\ensuremath{\xi}}_{l}]$, where a is the lattice spacing. For systems with mobility edge, we find analytic relations between $I(\ensuremath{\infty})$, the effective localization length ${\overline{\ensuremath{\xi}}}_{l}$, and the fraction of localized states fl. The imbalance as a function of disorder shows nonanalytic behavior when the mobility edge passes through a band edge. For interacting bosonic systems, we show that there is a mechanism to retain a finite long-time imbalance in the system even in presence of dissipative and stochastic processes coming from interparticle scattering. The scattering of particles, which lead to a decay of the memory of initial conditions through dissipative processes, also creates excitations in the system. For strong disorder, the excitations act as a local bath, whose noise correlators retain information of the initial pattern. This sustains a finite imbalance at long times in strongly disordered interacting systems.
We study time dynamics of 1D disordered Heisenberg spin-1/2 chain focusing on a regime of large system sizes and a long time evolution. This regime is relevant for observation of many-body localization (MBL), a phenomenon that is expected to freeze the dynamics of the system and prevent it from reaching thermal equilibrium. Performing extensive numerical simulations of the imbalance, a quantity often employed in the experimental studies of MBL, we show that the regime of a slow power-law decay of imbalance persists to disorder strengths exceeding by at least a factor of 2 the current estimates of the critical disorder strength for MBL. Even though we investigate time evolution up to few thousands tunneling times, we observe no signs of the saturation of imbalance that would suggest freezing of system dynamics and provide a smoking gun evidence of MBL. We demonstrate that the situation is qualitatively different when the disorder is replaced by a quasiperiodic potential. In this case, we observe an emergence of a pattern of oscillations of the imbalance that is stable with respect to changes in the system size. This suggests that the dynamics of quasiperiodic systems remain fully local at the longest time scales we reach provided that the quasiperiodic potential is sufficiently strong. Our study identifies challenges in an unequivocal experimental observation of the phenomenon of MBL.
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) has emerged as a novel paradigm for robust ergodicity breaking in closed quantum many-body systems. However, it is not yet clear to which extent MBL survives in the presence of dissipative processes induced by the coupling to an environment. Here we study heating and ergodicity for a paradigmatic MBL system-an interacting fermionic chain subject to quenched disorder-in the presence of dephasing. We find that, even though the system is eventually driven into an infinite-temperature state, heating as monitored by the von Neumann entropy can progress logarithmically slowly, implying exponentially large time scales for relaxation. This slow loss of memory of initial conditions makes signatures of nonergodicity visible over a long, but transient, time regime. We point out a potential controlled realization of the considered setup with cold atomic gases held in optical lattices.