Delocalization effects and charge reorganizations induced by repulsive interactions in strongly disordered chains

Abstract

Abstract. We study the delocalization effect of a short-range repulsive interaction on the ground state of a finite density of spinless fermions in strongly disordered one dimensional lattices. The density matrix renormalization group method is used to explore the charge density and the sensitivity of the ground state energy with respect to the boundary condition (the persistent current) for a wide range of parameters (carrier density, interaction and disorder). Analytical approaches are developed and allow to understand some mechanisms and limiting conditions. For weak interaction strength, one has a Fermi glass of Anderson localized states, while in the opposite limit of strong interaction, one has a correlated array of charges (Mott insulator). In the two cases, the system is strongly insulating and the ground state energy is essentially invariant under a twist of the boundary conditions. Reducing the interaction strength from large to intermediate values, the quantum melting of the solid array gives rise to a more homogeneous distribution of charges, and the ground state energy changes when the boundary conditions are twisted. In individual chains, this melting occurs by abrupt steps located at sample-dependent values of the interaction where an (avoided) level crossing between the ground state and the first excitation can be observed. Important charge reorganizations take place at the avoided crossings and the persistent currents are strongly enhanced around the corresponding interaction value. These large delocalization effects become smeared and reduced after ensemble averaging. They mainly characterize half filling and strong disorder, but they persist away of this optimal condition. PACS. 72.15.-v Electronic conduction in metals and alloy -73.20.Dx Electron states in low-dimensional structures -72.10.Bg General formulation of transport theory -05.60.Gg Quantum transport

Persistent current and Drude weight in mesoscopic rings

“…A calculation of the finite-size corrections to the spin stiffness in a pure spin-1/2 XXZ chain, 37−39 has revealed a scaling behaviour in the gapped phase that has a similar form to the one found in our work. The result that the Drude weight in a ring in the gapless phase with an impurity scales to zero, is in agreement with a previous result obtained for a spin chain, 35 and with renormalization group arguments, which state that the impurity term is relevant leading to a transmission cut. 30,31 The observation that with disorder in the system, the interaction always leads to an additional decrease of the current and the Drude weight is also in agreement with previous results by other authors, 7,8 and can be understood as it is more difficult to move correlated electrons in a random potential than independent electrons.…”

Residual conductance of correlated one-dimensional nanosystems: A numerical approach

“…As our results demonstrate, the same effects can be found in the conductance g. Considering a given nanosystem, one observes a similar resonance structure [12] as for the persistent current [32,33], although the individual peaks are wider for the conductance than for the persistent current.…”

“…The charge reorganization induced by repulsive interactions in strongly disordered systems and its associated delocalization effect was first observed in the persistent current of nanosystems [32,33] forming a ring (without the auxiliary lead introduced within the embedding approach). As our results demonstrate, the same effects can be found in the conductance g. Considering a given nanosystem, one observes a similar resonance structure [12] as for the persistent current [32,33], although the individual peaks are wider for the conductance than for the persistent current.…”

Disorder and interactions in one-dimensional systems

“…9 contain many more points than in previous work and refer to significantly larger samples. 7,14,19,22,23 It should be noted in particular that the limit of the delocalized regime around W = 2.5 is a factor of 2 higher than predicted by Schmitteckert et al but lower than in earlier work. 19 …”

“…7,14,22,23 The first study examining Anderson localization 14 was on chains extending up to 60 lattice sites. The degree of localization was measured by the phase sensitivity to boundary conditions.…”