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arXiv:cond-mat/9511038 · Europhysics Letters (EPL)

Interaction-Induced Delocalization of Quasiparticle Pairs in the Anderson Insulator

Felix von Oppen, Tilo Wettig B

Published Dec 20, 1995• 27 citations
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Abstract

It has recently been established that a short-range interaction can strongly delocalize a pair of particles moving in a disordered potential. We investigate whether an analogous effect exists also for pairs of quasiparticles in the Anderson insulator by employing an approximate numerical evaluation of the two-particle Green function of the many-body system. At the Fermi energy, the quasiparticle pair is localized on the scale of the single-particle localization length. The delocalization effect is recovered when the excitation energy of the pair is comparable to the bandwidth.

DOI
10.1209/0295-5075/32/9/007

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It has recently been established that a short-range interaction can strongly delocalize a pair of particles moving in a disordered potential. We investigate whether an analogous effect exists also for pairs of quasiparticles in the Anderson insulator by employing an approximate numerical evaluation of the two-particle Green function of the many-body system. At the Fermi energy, the quasiparticle pair is localized on the scale of the single-particle localization length. The delocalization effect is recovered when the excitation energy of the pair is comparable to the bandwidth.
Abstract We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of metal-insulator phase transitions for the pair in two-(2D) and three-dimensional (3D) disordered lattices. In two dimensions, we find that interactions cause an exponential enhancement of the pair localization length with respect to its single-particle counterpart, but do not induce a delocalization transition. In particular we show that previous claims of 2D interaction-induced Anderson transitions are the results of strong finite-size effects. In three dimensions we find that the pair undergoes a metal-insulator transition belonging to the same (orthogonal) universality class of the noninteracting model. We then explore the phase diagram in the space of energy E, disorder W and interaction strength U, which reveals a rich and counterintuitive structure, endowed with multiple metallic and insulating phases. We point out that this phenomenon originates from the molecular and scattering-like nature of the pair states available at given energy and disorder strength.
The localization properties of quasiparticle pairs above a frozen Fermi sea in the two- and three-dimensional Anderson model with Hubbard interaction are investigated. The dependence of the width Γ of the local spectral density on the pair excitation energy ε2, the disorder W, the interaction strength U and the linear system size L is determined. The obtained results allow to emphasize an interaction-induced pair delocalization effect even when the quasiparticles remain individually localized. The corresponding mobility edge is further estimated and the disorder versus interaction phase diagram is determined. Further investigations focusing on the spectral properties of the system and the transition from Poisson to Wigner-Dyson statistics corroborate these conclusions. The relevance of this effect with respect to the one-quasiparticle lifetime is finally discussed.
We investigate Anderson localization of two particles moving in a two-dimensional (2D) disordered lattice and coupled by contact interactions. Based on transmission-amplitude calculations for relatively large strip-shaped grids, we find that all pair states are localized in lattices of infinite size. In particular, we show that previous claims of an interaction-induced mobility edge are biased by severe finite-size effects. The localization length of a pair with zero total energy exhibits a nonmonotonic behavior as a function of the interaction strength, characterized by an exponential enhancement in the weakly interacting regime. Our findings also suggest that the many-body mobility edge of the 2D Anderson-Hubbard model disappears in the zero-density limit, irrespective of the (bosonic or fermionic) quantum statistics of the particles.
We show that the crossover from the weak interaction limit towards the strong interaction limit may be accompanied by a delocalization effect in one dimensional disordered quantum models. The spin degrees of freedom are frozen and the spatial wave functions remain symmetric or antisymmetric when the strength U of a short range interaction is varied. The study concerns the excited states for two interacting particles and the ground state for a finite density of carriers. First, for two particles in a chain of length L, we establish a duality transformation mapping the behavior at weak U onto the behavior at strong U. For intermediate U, the mixing of the one body states and the interaction induced delocalization effect are maximum. Furthermore, if L ≈︂ L1 (the one particle localization length), the system becomes weakly chaotic with critical spectral statistics. This weak chaos is related to the multifractality of the interaction matrix. For two particles starting close to each other, localization is reached in two steps. Before the time t1 necessary to propagate over L1 , U de-favors the propagation. On the contrary, U favors a very slow delocalization after t1 , characterized by a log(t) spreading of the center of mass. Similarly, the curvatures of the energy levels with respect to an enclosed magnetic flux decrease as a function of U for L < L1 and increase for L > L1 . The changes of the curvatures can be described by a conductance-like single scaling parameter. Second, using the density renormalization group algorithm, we have studied the ground state energy of a finite density of spinless fermions and its change under twisted boundary conditions. For a large disorder, a charge reorganization is induced by the interaction: When the system becomes instable between the inhomogeneous configuration driven by the random potential (Anderson insulator) and the homogeneous one driven by repulsive interactions (Mott insulator), the ground state sensitivity can be enhanced by orders of magnitude. In contrast, no enhancement occurs at weaker disorder, when there are many particles on a scale L1.
We consider ddd-dimensional systems which are localized in the absence of interactions, but whose single-particle localization length diverges near a discrete set of (single-particle) energies, with critical exponent $\ensuremath{\nu}$. This class includes disordered systems with intrinsic or symmetry protected topological bands, such as disordered integer quantum Hall insulators. We show that such marginally localized systems exhibit anomalous properties intermediate between localized and extended, including vanishing dc conductivity but subdiffusive dynamics, and fractal entanglement (an entanglement entropy with a scaling intermediate between area and volume law). We investigate the stability of marginal localization in the presence of interactions, and argue that arbitrarily weak short-range interactions trigger delocalization for partially filled bands at nonzero energy density if $\ensuremath{\nu}\ensuremath{\ge}1/d$. We use the Harris-Chayes bound $\ensuremath{\nu}\ensuremath{\ge}2/d$ to conclude that marginal localization is generically unstable in the presence of interactions. Our results suggest the impossibility of stabilizing quantized Hall conductance at nonzero energy density.
Anderson localization1 in a random system is sensitive to a distance dependence of the excitation transfer amplitude V(r). If V(r) decreases with the distance r slower than 1/r^d in a d-dimensional system then all excitations are delocalized at arbitrarily strong disordering, due to the resonant interaction of far separated quantum states (Fig. 1). At finite temperature T>0 the density of excitations is finite and they can influence each other by means of their interaction. Many body excitations involving simultaneous transitions of several single particle excitations create additional channels for energy delocalization and transport. Here we show that if the interaction of excitations decreases with the distance slower than 1/R^(2d) then excitations are delocalized at finite temperature irrespectively to disordering. This delocalization results in the finite decoherence rate in the ensemble of interacting spins 1/2 representing the model of quantum computer, thus restricting the quantum hardware performance. It also leads to the energy and particle delocalization and transport at finite temperature in various physical systems including doped semiconductors, despite of the full localization of electrons at zero temperature.