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arXiv:cond-mat/9806194 · Physical Review Letters

Do Interactions Increase or Reduce the Conductance of Disordered Electrons? It Depends!

Thomas Vojta, Frank Epperlein, Michael Schreiber

Published Nov 9, 1998• 71 citations
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Abstract

We investigate the influence of electron-electron interactions on the conductance of two-dimensional disordered spinless electrons. We present an efficient numerical method based on diagonalization in a truncated basis of Hartree-Fock states to determine with high accuracy the low-energy properties in the entire parameter space. We find that weak interactions increase the dc conductance in the strongly localized regime while they decrease the dc conductance for weak disorder. Strong interactions always decrease the conductance. We also study the localization of single-particle excitations at the Fermi energy which turns out to be only weakly influenced by the interactions.

DOI
10.1103/physrevlett.81.4212

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We investigate the influence of electron-electron interactions on the conductance of two-dimensional disordered spinless electrons. We present an efficient numerical method based on diagonalization in a truncated basis of Hartree-Fock states to determine with high accuracy the low-energy properties in the entire parameter space. We find that weak interactions increase the dc conductance in the strongly localized regime while they decrease the dc conductance for weak disorder. Strong interactions always decrease the conductance. We also study the localization of single-particle excitations at the Fermi energy which turns out to be only weakly influenced by the interactions.
We numerically investigate the transport properties of interacting spinless electrons in disordered systems. We use an efficient method which is based on the diagonalization of the Hamiltonian in the subspace of the many-particle Hilbert space which is spanned by the low-energy Slater states. Low-energy properties can be calculated with an accuracy comparable to that of exact diagonalization but for larger system sizes. The method works well in the entire parameter space, and it can handle long-range as well as short-range interactions. Using this method we calculate the combined effect of disorder and interactions on the Kubo-Greenwood conductance and on the sensitivity of the ground state energy to a twist in the boundary conditions. We find that the influence of the interactions on the transport properties is opposite for large and small disorder. In the strongly localized regime (small kinetic energy, large disorder) interactions increase the transport whereas for weak disorder (large kinetic energy) interactions decrease the transport.
We numerically investigate the transport properties of disordered interacting electrons in three dimensions in the metallic as well as in the insulating phases. The disordered many-particle problem is modeled by the quantum Coulomb glass which contains a random potential, long-range unscreened Coulomb interactions and quantum hopping between different sites. We have recently developed the Hartree-Fock based diagonalization (HFD) method which amounts to diagonalizing the Hamiltonian in a suitably chosen energetically truncated basis. This method allows us to investigate comparatively large systems. Here we calculate the combined effect of disorder and interactions on the dissipative conductance. We find that the qualitative influence of the interactions on the conductance depends on the relative disorder strength. For strong disorder interactions can significantly enhance the transport while they suppress the conductance for weak disorder.
Abstract We numerically investigate the transport properties of disordered interacting electrons in three dimensions in the metallic as well as in the insulating phases. The disordered many‐particle problem is modeled by the quantum Coulomb glass which contains a random potential, long‐range unscreened Coulomb interactions and quantum hopping between different sites. We have recently developed the Hartree‐Fock based diagonalization (HFD) method which amounts to diagonalizing the Hamiltonian in a suitably chosen energetically truncated basis. This method allows us to investigate comparatively large systems. Here we calculate the combined effect of disorder and interactions on the dissipative conductance. We find that the qualitative influence of the interactions on the conductance depends on the relative disorder strength. For strong disorder interactions can significantly enhance the transport while they suppress the conductance for weak disorder.
We consider the combined influence of disorder, electron-electron interactions and quantum hopping on the properties of electronic systems in a localized phase, approaching an insulator-metal transition.The generic models in this regime are the quantum Coulomb glass and its generalization to electrons with spin.After introducing these models we explain our computational method, the Hartree-Fock based diagonalization.We then discuss the conductance and compare spinless fermions and electrons.It turns out that spin degrees of freedom do not play an essential role in the systems considered.Finally, we analyze localization and decay of singleparticle excitations.We find that interactions generically tend to localize these excitations which is a result of the Coulomb gap in the single-particle density of states.
We consider the combined influence of disorder, electron4ectron interactions and quantum hopping on the properties of electronic systems in a localized phase, approaching an insulator-metal transition. The generic models in this regime are the quantum Coulomb glass and its generalization to electrons with spin. After introducing these models we explain our computational method, the Hartree-Fock-based diagonalization. We then discuss the conductance and compare spinless fermions and electrons. It turns out that spin degrees of freedom do not play an essential role in the systems considered. Finally, we analyse localization and decay of single-particle excitations. We find that interactions generically tend to localize these excitations, which is a result of the Coulomb gap in the single-particle density of states.
Dynamical conductivity in a disordered one-dimensional model of interacting fermions is studied numerically at high temperatures and in the weak-interaction regime in order to find a signature of many-body localization and vanishing dc transport coefficients. On the contrary, we find in the regime of moderately strong local disorder that the dc conductivity ${\ensuremath{\sigma}}_{0}$ scales linearly with the interaction strength while being exponentially dependent on the disorder. According to the behavior of the charge stiffness evaluated at the fixed number of particles, the absence of the many-body localization seems related to an increase in the effective localization length with the interaction.