Many localized electrons in disordered systems with Coulomb interaction: A simulation of the Coulomb glass

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Abstract
The low-temperature properties of the Coulomb glass, i.e., a disordered system with many electrons subject to long-range electron-electron interaction, are investigated by means of a Monte Carlo simulation. The Metropolis algorithm enables a systematic analysis of three-dimensional systems with up to 256 electrons on 512 sites within the standard lattice model for compensated doped semiconductors. We obtain the thermodynamical properties like the expectation value of the internal energy and the specific heat with high accuracy. A modification of the algorithm yields the spectrum of the low-energy many-electron excitations. The majority of these excitations is characterized by a correlated displacement of several electrons which often span the size of the entire system. A detailed analysis of the correlations corroborates the importance of variable-number hopping, while variable-range hopping is insignificant for low temperatures due to the lack of possible final states. Accordingly the density of states of the correlated many-electron excitations displays a soft gap in correspondence to the Coulomb gap known for the single-electron density of states.

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