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… Show more
“…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.…”
We study the persistent current and the Drude weight of a system of spinless fermions, with repulsive interactions and a hopping impurity, on a mesoscopic ring pierced by a magnetic flux, using a Density Matrix Renormalization Group algorithm for complex fields. Both the Luttinger Liquid (LL) and the Charge Density Wave (CDW) phases of the system are considered. Under a Jordan-Wigner transformation, the system is equivalent to a spin-1/2 XXZ chain with a weakened exchange coupling. We find that the persistent current changes from an algebraic to an exponential decay 1 as the system crosses from the LL to the CDW phase, with increasing interaction U . We also find that in the interacting system the persistent current is invariant under the impurity transformation ρ → 1/ρ, for large system sizes, where ρ is the defect strength. The persistent current exhibits a scaling behaviour that is in agreement with the scaling behaviour obtained for the Drude weight. We find that in the LL phase the Drude weight scales with the number of lattice sites N as D ∼ N −α , with α > 0 due to the interplay of the electron interaction with the impurity, while in the CDW phase it scales as D ∼ N −δ exp(−N/ξ), ξ being a localization length and δ an exponent which both decrease with increasing interaction and impurity strength. Our results show that disorder and interactions always decrease the persistent current, and imply that the Drude weight vanishes in the limit N → ∞, in both phases.
“…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.…”
We study the persistent current and the Drude weight of a system of spinless fermions, with repulsive interactions and a hopping impurity, on a mesoscopic ring pierced by a magnetic flux, using a Density Matrix Renormalization Group algorithm for complex fields. Both the Luttinger Liquid (LL) and the Charge Density Wave (CDW) phases of the system are considered. Under a Jordan-Wigner transformation, the system is equivalent to a spin-1/2 XXZ chain with a weakened exchange coupling. We find that the persistent current changes from an algebraic to an exponential decay 1 as the system crosses from the LL to the CDW phase, with increasing interaction U . We also find that in the interacting system the persistent current is invariant under the impurity transformation ρ → 1/ρ, for large system sizes, where ρ is the defect strength. The persistent current exhibits a scaling behaviour that is in agreement with the scaling behaviour obtained for the Drude weight. We find that in the LL phase the Drude weight scales with the number of lattice sites N as D ∼ N −α , with α > 0 due to the interplay of the electron interaction with the impurity, while in the CDW phase it scales as D ∼ N −δ exp(−N/ξ), ξ being a localization length and δ an exponent which both decrease with increasing interaction and impurity strength. Our results show that disorder and interactions always decrease the persistent current, and imply that the Drude weight vanishes in the limit N → ∞, in both phases.
“…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.…”
Section: Conductance For Disordered Nanosystemssupporting
confidence: 81%
“…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.…”
Section: Conductance For Disordered Nanosystemsmentioning
Abstract. We study a method to determine the residual conductance of a correlated system by means of the ground-state properties of a large ring composed of the system itself and a long non-interacting lead. The transmission probability through the interacting region and thus its residual conductance is deduced from the persistent current induced by a flux threading the ring. Density Matrix Renormalization Group techniques are employed to obtain numerical results for one-dimensional systems of interacting spinless fermions. As the flux dependence of the persistent current for such a system demonstrates, the interacting system coupled to an infinite non-interacting lead behaves as a non-interacting scatterer, but with an interaction dependent elastic transmission coefficient. The scaling to large lead sizes is discussed in detail as it constitutes a crucial step in determining the conductance. Furthermore, the method, which so far had been used at half filling, is extended to arbitrary filling and also applied to disordered interacting systems, where it is found that repulsive interaction can favor transport.
“…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 …”
Section: B Disorder-interaction Phase Spacecontrasting
confidence: 50%
“…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.…”
We present a numerical approach to the study of disorder and interactions in quasi-one-dimensional ͑1D͒ systems which combines aspects of the transfer matrix method and the density matrix renormalization group which have been successfully applied to disorder and interacting problems, respectively. The method is applied to spinless fermions in 1D, and the existence of a conducting state is demonstrated in the presence of attractive interactions.
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