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arXiv:cond-mat/9804053 · Physical Review Letters

From the Fermi Glass towards the Mott Insulator in One Dimension: Delocalization and Strongly Enhanced Persistent Currents

Peter Schmitteckert, Rodolfo A. Jalabert, Dietmar Weinmann A, Jean‐Louis Pichard

Published Sep 14, 1998• 65 citations
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Abstract

When a system of spinless fermions in a disordered mesoscopic ring becomes unstable between the inhomogeneous configuration driven by the random potential (Anderson insulator) and the homogeneous one driven by repulsive interactions (Mott insulator), the persistent current can be enhanced by orders of magnitude. This is illustrated by a study of the change of the ground state energy under twisted boundary conditions using the density matrix renormalization group algorithm.

DOI
10.1103/physrevlett.81.2308

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When a system of spinless fermions in a disordered mesoscopic ring becomes unstable between the inhomogeneous configuration driven by the random potential (Anderson insulator) and the homogeneous one driven by repulsive interactions (Mott insulator), the persistent current can be enhanced by orders of magnitude. This is illustrated by a study of the change of the ground state energy under twisted boundary conditions using the density matrix renormalization group algorithm.
We consider the ground state reorganization driven by an increasing nearest neighbor repulsion U for spinless fermions in a strongly disordered ring. When U -> 0, the electrons form a glass with Anderson localized states. At half filling, a regular array of charges (Mott insulator) is pinned by the random substrate when U -> \infty. Between those two insulating limits, we show that there is an intermediate regime where the electron glass becomes more liquid before crystallizing. The liquid-like behavior of the density-density correlation function is accompanied by an enhancement of the persistent current.
Extending the finite-size scaling theory to the many-body ground state, one finds that Coulomb repulsion can drive a system of spinless fermions in a random potential from the Anderson insulator (Fermi glass of localized states) towards a new extended phase in dimension d = 2. The transition occurs at a Coulomb energy to Fermi energy ratio r s ≈ 4, where a change in the nature of the persistent currents has been previously observed. Relevance to the recently observed 2 d metallic phase is suggested.
Persistent currents flowing through disordered mesoscopic rings threaded by a magnetic flux are investigated. Models of fermions with on-site interactions (Hubbard model) or models of spinless fermions with nearest neighbor interactions are considered on 2D cylinders with twisted boundary conditions in one direction to account for a magnetic flux. Self-consistent Hartree-Fock methods are used to treat the electron-electron interaction beyond first order. We show that the second harmonic of the current (which is relevant in the diffusive regime) is {\it strongly suppressed} by the interaction in the case of spinless fermions while it is {\it significantly enhanced} in the Hubbard model. Our data also strongly suggest that the reduction (increase) of this harmonic is related to a strong increase (reduction) of the spacial fluctuations of the charge density.
Persistent currents flowing through disordered mesoscopic rings threaded by a magnetic flux are investigated. Models of fermions with on-site interactions (Hubbard model) or models of spinless fermions with nearest neighbor interactions are considered on 2D cylinders with twisted boundary conditions in one direction to account for a magnetic flux. Self-consistent Hartree-Fock methods are used to treat the electron-electron interaction beyond first order. We show that the second harmonic of the current (which is relevant in the diffusive regime) is strongly suppressed by the interaction in the case of spinless fermions while it is significantly enhanced in the Hubbard model. Our data also strongly suggest that the reduction (increase) of this harmonic is related to a strong increase (reduction) of the spatial fluctuations of the charge density.
We calculate the zero-temperature phase diagram of the disordered Bose-Hubbard model in one dimension using the density matrix renormalization group. For integer filling the Mott insulator is always separated from the superfluid by a Bose glass phase. There is a re-entrance of the Bose glass both as a function of the repulsive interaction and of disorder. At half-filling where no Mott insulator exists, the superfluid density has a maximum where the kinetic and repulsive energies are about the same. Superfluidity is suppressed both for small and very strong repulsion but is always monotonic in disorder.