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arXiv:1803.05974 · Physical review. E

Robustness of optimal transport in disordered interacting many-body networks

Adrián Ortega, Thomas Stegmann, Luis Benet

Published Jul 31, 2018• 9 citations
arXivHTMLPDF

Abstract

The robustness of quantum transport under various perturbations is analyzed in disordered interacting many-body systems, which are constructed from the embedded Gaussian random matrix ensembles (EGEs). The transport efficiency can be enhanced drastically, if centrosymmetry (csEGE) is imposed. When the csEGE is perturbed with an ordinary EGE, the transport efficiency in the optimal cases is reduced significantly, while in the suboptimal cases the changes are less pronounced. Qualitatively the same behavior is observed, when parity and centrosymmetry are broken by block perturbations. Analyzing the influence of the environment coupling, optimal transport is observed at a certain coupling strength, while too weak and too strong coupling reduce the transport. Taking into account the effects of decoherence, in the EGE the transport efficiency approaches its maximum at a finite nonzero decoherence strength (environment-assisted transport). In the csEGE the efficiency decays monotonically with the decoherence but is always larger than in the EGE.

DOI
10.1103/physreve.98.012141

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The robustness of quantum transport under various perturbations is analyzed in disordered interacting many-body systems, which are constructed from the embedded Gaussian random matrix ensembles (EGEs). The transport efficiency can be enhanced drastically, if centrosymmetry (csEGE) is imposed. When the csEGE is perturbed with an ordinary EGE, the transport efficiency in the optimal cases is reduced significantly, while in the suboptimal cases the changes are less pronounced. Qualitatively the same behavior is observed, when parity and centrosymmetry are broken by block perturbations. Analyzing the influence of the environment coupling, optimal transport is observed at a certain coupling strength, while too weak and too strong coupling reduce the transport. Taking into account the effects of decoherence, in the EGE the transport efficiency approaches its maximum at a finite nonzero decoherence strength (environment-assisted transport). In the csEGE the efficiency decays monotonically with the decoherence but is always larger than in the EGE.
The coherent transport of n fermions in disordered networks of l single-particle states connected by k-body interactions is studied. These networks are modeled by embedded Gaussian random matrix ensemble (EGE). The conductance bandwidth and the ensemble-averaged total current attain their maximal values if the system is highly filled n∼l-1 and k∼n/2. For the cases k=1 and k=n the bandwidth is minimal. We show that for all parameters the transport is enhanced significantly whenever centrosymmetric embedded Gaussian ensemble (csEGE) are considered. In this case the transmission shows numerous resonances of perfect transport. Analyzing the transmission by spectral decomposition, we find that centrosymmetry induces strong correlations and enhances the extrema of the distributions. This suppresses destructive interference effects in the system and thus causes backscattering-free transmission resonances that enhance the overall transport. The distribution of the total current for the csEGE has a very large dominating peak for n=l-1, close to the highest observed currents.
In finite many-body quantum systems such as nuclei, atoms, mesoscopic systems like quantum dots and small metallic grains, interacting spin systems modeling quantum computing core and BEC, the interparticle interactions are essentially two-body in nature. Therefore, it is more appropriate to represent the complex Hamiltonian of these systems by random ensembles that incorporate the two-body nature of interactions. These ensembles are generically called embedded Gaussian ensembles (EGEs). The aim of the present thesis is to identify and systematically analyze many different physically relevant EGEs with symmetries by considering a variety of quantities and measures that are important for isolated finite interacting quantum systems.
We study, under very general conditions and in a variety of geometries, quantum enhancement of transport in open systems. Both static disorder and dephasing associated with dynamical disorder (or finite temperature) are fully included in the analysis. We show that quantum coherence effects may significantly enhance transport in open quantum systems even in the semiclassical regime (where the decoherence rate is greater than the inter-site hopping amplitude), as long as the static disorder is sufficiently strong. When the strengths of static and dynamical disorder are fixed, there is an optimal opening strength at which the coherent transport enhancement is optimized. Analytic results are obtained in two simple paradigmatic tight-binding models of large systems: the linear chain and the fully connected network. The physical behavior is also reflected, for example, in the FMO photosynthetic complex, which may be viewed as being intermediate between these paradigmatic models. We furthermore show that a nonzero dephasing rate assists transport in an open linear chain when the disorder strength exceeds a critical value, and obtain this critical disorder strength as a function of the degree of opening.
Eigenstate structure in many-body bosonic systems: Analysis using random matrices and qqq-Hermite polynomials
We analyze the structure of eigenstates in many-body bosonic systems by modeling the Hamiltonian of these complex systems using Bosonic Embedded Gaussian Orthogonal Ensembles (BEGOE) defined by a mean-field plus kkk-body random interactions. The quantities employed are the number of principal components (NPC), the localization length (lHl_HlH​) and the entropy production S(t)S(t)S(t). The numerical results are compared with the analytical formulas obtained using random matrices which are based on bivariate qqq-Hermite polynomials for local density of states Fk(E∣q)F_k(E|q)Fk​(E∣q) and the bivariate qqq-Hermite polynomial form for bivariate eigenvalue density ρbiv:q(E,Ek)ρ_{biv:q}(E,E_k)ρbiv:q​(E,Ek​) that are valid in the strong interaction domain. We also compare transport efficiency in many-body bosonic systems using BEGOE in absence and presence of centrosymmetry. It is seen that the centrosymmetry enhances quantum efficiency.
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.
Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle (predom-inantly two-particle) interactions. The random matrix models incorporating the few-particle nature of interactions are known as embedded random matrix ensembles. In the present paper, we provide a brief overview of these two ensembles and illustrate how the embedded ensembles can be successfully used to study decoherence of a qubit interacting with an environment, both for fermionic and bosonic embedded ensembles. Numerical calculations show the dependence of decoherence on the nature of the environment.