Large system asymptotics of persistent currents in mesoscopic quantum rings

Abstract

We consider a one-dimensional mesoscopic quantum ring filled with spinless electrons and threaded by a magnetic flux, which carries a persistent current at zero temperature. The interplay of Coulomb interactions and a single on-site impurity yields a non-trivial dependence of the persistent current on the size of the ring. We determine numerically the asymptotic power law for systems up to 32 000 sites for various impurity strengths and compare with predictions from Bethe Ansatz solutions combined with Bosonization. The numerical results are obtained using an improved functional renormalization group (fRG) method. We apply the density matrix renormalization group (DMRG) and exact diagonalization methods to benchmark the fRG calculations. We use DMRG to study the persistent current at low electron concentrations in order to extend the validity of our results to quasi-continuous systems. We briefly comment on the quality of calculated fRG ground state energies by comparison with exact DMRG data.

Metal–insulator transition in an one-dimensional half-filled interacting mesoscopic ring with spinless fermions: Exact results

“…For W = 0 we get ξ = 1.5, while it is 1.4 for W = 2. Most notably, from our exhaustive numerical analysis we find that with increasing disorder strength ξ gradually decreases and eventually reach towards the limiting value 1.33, which is consistent with the asymptotic behavior as suggested by Gendiar et al 28 .…”

Efficient MPS Algorithm for Periodic Boundary Conditions and Applications Section: Solid matter Original Author's Text: English Abstract: We present the implementation of an efficient algorithm for the calculation of the spectrum of one-dimensional quantum systems with periodic boundary conditions. This algorithm is based on a matrix product representation for quantum states (MPS) and a similar representation for Hamiltonians and other operators (MPO). It is significantly more efficient for systems of abou

“…The energy determined for the ground state agrees with the result given in Ref. [8]. We also calculate the energy of the next higher/lower state and the number of particles n it contains.…”

“…[8] and the references therein. The Hamiltonian is U(1) symmetric, and the particle number is a good quantum number to label the states.…”

Functional renormalization group approach to correlated fermion systems

“…The functional RG results for a single local impurity in a LL show that the LSG model describes the physics (two fixed points, exponents, one-parameter scaling) of a broader class of models. The same approach was also used to study the persistent current through a LL ring with a local impurity prierced by a magnetic flux (Gendiar et al, 2009;Meden and Schollwöck, 2003a,b) Aspects resulting from the spin degree of freedom of electrons were discussed by Andergassen et al (2006a) and Andergassen et al (2006b).…”