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Register a new userControlled engineering of extended states in disordered systems
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We describe how to engineer wavefunction delocalization in disordered systems modelled by tight-binding Hamiltonians in d>1 dimensions. We show analytically that a simple product structure for the random onsite potential energies, together with suitably chosen hopping strengths, allows a resonant scattering process leading to ballistic transport along one direction, and a controlled coexistence of extended Bloch states and anisotropically localized states in the spectrum. We demonstrate that these features persist in the thermodynamic limit for a continuous range of the system parameters. Numerical results support these findings and highlight the robustness of the extended regime with respect to deviations from the exact resonance condition for finite systems. The localization and transport properties of the system can be engineered almost at will and independently in each direction. This study gives rise to the possibility of designing disordered potentials that work as switching devices and band-pass filters for quantum waves, such as matter waves in optical lattices.
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It is commonly believed that Anderson localized states and extended states do not coexist at the same energy. Here we propose a simple mechanism to achieve the coexistence of localized and extended states in a band in a class of disordered quasi-1D and quasi-2D systems. The systems are partially disordered in a way that a band of extended states always exists, not affected by the randomness, whereas the states in all other bands become localized. The extended states can overlap with the localized states both in energy and in space, achieving the aforementioned coexistence. We demonstrate such coexistence in disordered multi-chain and multi-layer systems.
We explore thermalization and quantum dynamics in a one-dimensional disordered SU(2)-symmetric Floquet model, where a many-body localized phase is prohibited by the non-abelian symmetry. Despite the absence of localization, we find an extended nonergodic regime at strong disorder where the system exhibits nonthermal behaviors. In the strong disorder regime, the level spacing statistics exhibit neither a Wigner-Dyson nor a Poisson distribution, and the spectral form factor does not show a linear-in-time growth at early times characteristic of random matrix theory. The average entanglement entropy of the Floquet eigenstates is subthermal, although violating an area-law scaling with system sizes. We further compute the expectation value of local observables and find strong deviations from the eigenstate thermalization hypothesis. The infinite temperature spin autocorrelation function decays at long times as $t^{-beta}$ with $beta < 0.5$, indicating subdiffusive transport at strong disorders.
We study the dynamics of one and two dimensional disordered lattice bosons/fermions initialized to a Fock state with a pattern of $1$ and $0$ particles on $A$ and ${bar A}$ sites. For non-interacting systems we establish a universal relation between the long time density imbalance between $A$ and ${bar A}$ site, $I(infty)$, the localization length $xi_l$, and the geometry of the initial pattern. For alternating initial pattern of $1$ and $0$ particles in 1 dimension, $I(infty)=tanh[a/xi_l]$, where $a$ is the lattice spacing. For systems with mobility edge, we find analytic relations between $I(infty)$, the effective localization length $tilde{xi}_l$ and the fraction of localized states $f_l$. The imbalance as a function of disorder shows non-analytic behaviour when the mobility edge passes through a band edge. For interacting bosonic systems, we show that dissipative processes lead to a decay of the memory of initial conditions. However, the excitations created in the process act as a bath, whose noise correlators retain information of the initial pattern. This sustains a finite imbalance at long times in strongly disordered interacting systems.
Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble- averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with the perturbation theory and isotropic entanglement theory.
Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or quantum computation. In this work we investigate an extended system of N qubits. In our system a qubit is the absence or presence of an electron at a site of a tight-binding system. Several measures of entanglement between a given qubit and the rest of the system and also the entanglement between two qubits and the rest of the system is calculated in a one-electron picture in the presence of disorder. We invoke the power law band random matrix model which even in one dimension is able to produce multifractal states that fluctuate at all length scales. The concurrence, the tangle and the entanglement entropy all show interesting scaling properties.
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