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Solid State Communications

Finite-size studies of the FQHE-electron solid phase transition using a non-orthogonal localised basis set

David A. W. Hutchinson, John C. Inkson, J.M. Rowe

Published Feb 1, 1996• 4 citations
Publisher
DOI
10.1016/0038-1098(95)00606-0

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The study of quantum transport is important for understanding the propagation of electronic currents in matter on nanoscopic and mesoscopic scales. We discuss the use of a novel orthogonal wavepacket basis set for non-equilibrium many-electron transport problems. The basis is constructed from stroboscopic images of the continuous time evolution of an initial set of wavepackets. This built-in time-related feature of the basis makes it efficient for practical computational schemes and also suitable for providing physical insight into transport phenomena. We demonstrate how the wavepacket basis can be used to recover the exact non-interacting ground state density for systems with a localised potential barrier. Using a Hartree-like electron-electron interaction, we then implement the basis in two 1D transport problems: the establishment of a steady current and the abrupt switching on of a potential barrier in a system in its ground state. Finally, we discuss the effect of spurious self-interaction on the propagation of the wavepackets.
This article outlines a tutorial review of some recent progress in the theory of phase transitions and criticality. Topics mentioned are: |φ|6 field theories in (d=3)-dimensional space which correspond to the limits of tricriticality in spherical models; the desirability of finding real systems displaying critical endpoints, etc., in a magnetic field; scaling theories for first-order magnetic transitions in block and cylinder geometries, including spin-wave contributions, ϵ=4 - d expansions for finite-size effects at and near criticality; the universal correlation length amplitude for critical-point correlations in a finite cylinder and its evaluation in d = 2 dimensions on the basis of conformal covariance; the predictions of conformal covariance for other finite-size and surface critical-point properties; the implications, stemming from field theory, of conformal covariance and unitarity for general criticality in two dimensions, including infinitely many sets of exact critical exponents for Ising-like, three-state Potts-like, … systems; the discovery of new, exactly soluble two-dimensional, “restricted solid-on-solid” models which display all the predicted conformally covariant multicritical points and a second infinite set as well!