We systematically investigate the interplay of disorder and time-homogeneous collisional noise in shaping the transport dynamics of an anisotropic XXZ spin chain. Using stochastic collision models to simulate interaction with the environment, we explore the localization-delocalization transitions across regimes with single and multiple excitations. We find that space-homogeneous and low-rate collisions can shape regions where localization sets in the form of subsequent plateaus. The localization process has universal features for the plateaus duration and the delocalization time. Interactions among the excitations favor this process even for tiniest disorder levels. Our findings can be applied to design stroboscopic protocols where sequences of transport and localization can be tailored. We establish relevant connections to noise-engineering of quantum devices in noisy intermediate-scale quantum simulators platforms, and to realistic biological systems where noise and disorder coexist.
We systematically investigate the interplay of disorder and time-homogeneous collisional noise in shaping the transport dynamics of an anisotropic XXZ spin chain. Using stochastic collision models to simulate interaction with the environment, we explore the localization-delocalization transitions across regimes with single and multiple excitations. We find that space-homogeneous and low-rate collisions can shape regions where localization sets in the form of subsequent plateaus. The localization process has universal features for the plateaus duration and the delocalization time. Interactions among the excitations favor this process even for tiniest disorder levels. Our findings can be applied to design stroboscopic protocols where sequences of transport and localization can be tailored. We establish relevant connections to noise-engineering of quantum devices in noisy intermediate-scale quantum simulators platforms, and to realistic biological systems where noise and disorder coexist.
The study of noise assisted-transport in quantum systems is essential in a wide range of applications, from near-term NISQ devices to models for quantum biology. Here, we study a generalized XXZ model in the presence of stochastic collision noise, which allows describing environments beyond the standard Markovian formulation. Our analysis through the study of the local magnetization, the inverse participation ratio (IPR) or its generalization, and the inverse ergodicity ratio (IER) showed clear regimes, where the transport rate and coherence time could be controlled by the dissipation in a consistent manner. In addition, when considering various excitations, we characterized the interplay between collisions and system interactions, identifying regimes in which transport was counterintuitively enhanced when increasing the collision rate, even in the case of initially separated excitations. These results constitute an example of an essential building block for the understanding of quantum transport in structured noisy and warm-disordered environments.
The interplay between interaction, disorder, and dissipation has shown a rich phenomenology. Here, we investigate a disordered XXZ spin chain in contact with a bath which, alone, would drive the system toward a highly delocalized and coherent Dicke state. We show that there exist regimes for which the natural orbitals of the single-particle density matrix of the steady state are all localized in the presence of strong disorders, for either weak interaction or strong interaction. We show that the averaged steady-state occupation in the eigenbasis of the open system Hamiltonian could follow an exponential decay for intermediate disorder strength in the presence of weak interactions, while it is more evenly spread for strong disorder or for stronger interactions. Last, we show that strong dissipation increases the coherence of the steady states, thus reducing the signatures of localization. We capture such signatures of localization also with a concatenated inverse participation ratio that simultaneously takes into account how localized are the eigenstates of the Hamiltonian and how close is the steady state to an incoherent mixture of different energy eigenstates.
Many types of dissipative processes can be found in nature or be engineered, and their interplay with a system can give rise to interesting phases of matter. Here we study the interplay among interaction, tunneling, and disorder in the steady state of a spin chain coupled to a tailored bath. We consider a dissipation which, in contrast to disorder, tends to generate a homogeneously polarized steady state. We find that the steady state can be highly sensitive even to weak disorder. We also establish that, in the presence of such dissipation, even in the absence of interaction, a finite amount of disorder is needed for localization. Last, we show that for strong disorder the system reveals signatures of localization both in the weakly and strong interacting regimes.
While there are well-established methods to study delocalization transitions of single particles in random systems, it remains a challenging problem how to characterize many-body delocalization transitions. Here, we use a generalized real-space renormalization group technique to study the anisotropic Heisenberg model with long-range interactions, decaying with a power α , which are generated by placing spins at random positions along the chain. This method permits a large-scale finite-size scaling analysis. We examine the full distribution function of the excitation energy gap from the ground state and observe a crossover with decreasing α . At α c the full distribution coincides with a critical function. Thereby, we find strong evidence for the existence of a many-body localization transition in disordered antiferromagnetic spin chains with long-range interactions.
Quantum transport in disordered systems poses intriguing fundamental questions about the interplay of disorder, interactions, and decoherence, with important implications for nanoscale energy transfer and quantum information transfer. Here, we investigate the emergence of multiple transport timescales in the dissipative dynamics of a spin impurity coupled to a small, spatially disordered network of spins. Using a two-dimensional tight-binding model with dipolar interactions and local dephasing, we demonstrate that geometric heterogeneity leads to hierarchical coupling strengths and pronounced separation of dynamical timescales. By analyzing different metrics for dynamics, we identify distinct relaxation timescales associated with cluster-level equilibration and global equilibration. A minimal three-site model reveals the physical origin of the longest timescale: strong internal hybridization generates an effective detuning that suppresses transfer to other weakly coupled sites, yielding a parametrically enhanced relaxation time in the weak-dephasing regime. We corroborate this picture with nonequilibrium steady-state transport calculations and simulations of disordered spin configurations, demonstrating orders-of-magnitude slowing of relaxation when hierarchical couplings are present. Our results highlight the central role of geometry and connectivity in spin networks and open quantum systems in general, and provide experimentally relevant predictions for relaxation times in small spin baths.
Within the broad theme of understanding the dynamics of disordered quantum many-body systems, one of the simplest questions one can ask is, given an initial state, how does it evolve in time on the associated Fock-space graph, in terms of the distribution of probabilities thereon? A detailed quantitative description of the temporal evolution of out-of-equilibrium disordered quantum states and probability transport on the Fock space is our central aim here. We investigate it in the context of a disordered quantum spin chain, which hosts a disorder-driven many-body localization transition. Real-time dynamics/probability transport is shown to exhibit a rich phenomenology, which is markedly different between the ergodic and many-body localized phases. The dynamics is, for example, found to be strongly inhomogeneous at intermediate times in both phases, but while it gives way to homogeneity at long times in the ergodic phase, the dynamics remain inhomogeneous and multifractal in nature for arbitrarily long times in the localized phase. Similarly, we show that an appropriately defined dynamical lengthscale on the Fock-space graph is directly related to the local spin autocorrelation, and as such sheds light on the (anomalous) decay of the autocorrelation in the ergodic phase, and lack of it in the localized phase.