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physica status solidi (b)

Low‐energy spectrum of one‐dimensional generalized Wigner lattice

Victor V. Slavin

Published Jul 4, 2005• 3 citations
Publisher

Abstract

Abstract The low‐energy spectrum of one‐dimensional lattice electron system with long‐range inter‐electron repulsion is studied at arbitrary electron concentration, ρ. It is established that the value of the gap in this spectrum is an oscillating function of inverse electron concentration. This value tends to zero at ρ = 1/q (q = 1, 2 …), reaching the maximum at ρ = 2/(2q + 1). It is shown that the low‐energy spectrum of the system under consideration may be described in terms of one‐dimensional structures which are analogues of domains in one‐dimensional spin systems. The question about these “domains” decay is considered. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200440068

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Abstract New analytical results are obtained for the Green's function of a finite one‐dimensional lattice with nearest neighbor interaction using discrete Fourier transform. The method offers an alternative to the Bethe Ansatz, but does not require any a priori assumption on the form of the wavefunction. This makes it suitable for extensions to nano‐ferromagnets of higher dimensions. Solutions of the Heisenberg spin chain with periodic and open boundary conditions are considered as examples. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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The low-temperature thermodynamics of a one-dimensional electron gas on a disordered lattice, which comes to existence when the inter-electron distances exceed noticeably the inter-site ones, has been studied. An efficient computer procedure, based on the presentation of the partition function as a product of random transfer-matrixes, has been developed for calculations of thermodynamic characteristics of the system under consideration. The lattice structures were varied from completely chaotic up to the strictly regular one. It has been established that for any degree of disorder the entropy and heat capacity of the system tend to zero linearly as the temperature is reduced. The conclusion about the gapless character of the elementary excitations spectrum has been made. An instability of one-dimensional electron gas on a disordered lattice has been revealed: under conditions of vanishingly small disordering of the lattice, the long-range order in the systems under consideration is broken by frustrations that are one-dimensional analogues of the frustrations in two- and three-dimensional spin glasses.
A one-dimensional gas of electrons interacting with long-range Coulomb forces [V(r)\ensuremath{\approxeq}1/r] is investigated. The excitation spectrum consists of separate collective charge and spin modes. For arbitrarily weak Coulomb repulsion density correlations at wave vector 4kF{\mathit{k}}_{\mathit{F}}kF​ decay extremely slowly and are best described as those of a one-dimensional Wigner crystal. Pinning of the Wigner crystal then leads to the nonlinear transport properties characteristic of charge density waves. The results allow a consistent interpretation of the plasmon and spin excitations observed in one-dimensional semiconductor structures, and suggest an interpretation of some of the observed features in terms of ``spinons.''
Abstract A refined variational wave function for the two‐dimensional repulsive Hubbard model is studied numerically, with the aim of approaching the difficult crossover regime of intermediate values of U. The issue of a superconducting ground state with d‐wave symmetry is investigated for an average electron density n ≈ 0.8 and for U = 8t. Due to finite‐size effects a clear‐cut answer to this fundamental question has not yet been reached. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)