Persistent current and Drude weight in mesoscopic rings

Abstract

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.

Persistent current and Drude weight for the one-dimensional Hubbard model from current lattice density functional theory

“…It is well known that j is strongly size dependent, since it originates from electron coherence across the entire ring [30]. For a perfect metal one expect j to scale as 1/L [25].…”

“…A similar approach has been earlier used to study the effect of disorder on persistent current for the Hubbard model at half-filling [70]. Recently a density matrix renormalization group algorithm has been developed to deal with complex Hamiltonian matrices and used to calculate D c for spinless fermions [30].…”

“…In both frameworks exact diagonalization (ED) has been the preferential solving strategy for small systems (small number of sites and electrons) [19,25]. Additional methods used to study quantum rings over lattice models include the Bethe ansatz (BA) [26,27], renormalization group [28] and density matrix renormalization group [29,30]. In contrast, the continuum model has been tackled with self-consistent Hartree-Fock techniques [31], bosonization schemes [32], conformal field theory [33], current-spin density functional theory [34] and quantum Monte Carlo methods [35].…”

Many-body-localization transition: sensitivity to twisted boundary conditions

“…Its statistical properties have been much studied in chaotic quantum systems and random matrices [6][7][8][9][10] and in Anderson Localization models [11][12][13][14][15][16][17]. The case of the ground state energy in interacting quantum models has been analyzed both without disorder [18,19] and with disorder [20][21][22], in particular to characterize the persistent currents induced by a magnetic flux in mesoscopic rings. The case of highly excited eigenstates in a disordered model of interactions fermions has been investigated very recently [23] in the context of the Many-Body-Localization problem (see the recent reviews [24,25] and references therein).…”

Drude weight increase by orbital and repulsive interactions in fermionic ladders

“…It is thus important, both on the experimental and fundamental level, to understand and develop physical intuition concerning the effects of strong correlations on the Drude weight. It is commonly believed that repulsive interactions reduce particle mobility in a many-body system, leading to a generic reduction of the Drude weight [15,[35][36][37]. Nevertheless, it was recently observed that this fact is remarkably violated in Creutz ladders [38]: this was attributed to the presence of an isolated Dirac cone and put into relation to the anomalous magnetic orbital response of 2D graphene [39].…”