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Physical review. B, Condensed matter

Band-filling and magnetic-field effects on the phase diagram of one-dimensional conductors

Gilles Montambaux, M. Héritier, Pascal Lederer

Published Jun 1, 1986• 11 citations
Publisher

Abstract

We investigate the Fermi gas model for one-dimensional (1D) conductors as a function of chemical potential and of the applied magnetic field. The bosonization method allows to prove the equivalence between these parameters, the first acting on charge degrees of freedom, the second on spin degrees of freedom. A number of results available in the literature can thus be connected. We also use the mapping to the 2D classical Coulomb gas and a two-cutoff renormalization-group method, the two energy scales being the bandwidth and the Zeeman energy (or the chemical potential). We obtain a coherent description of the Fermi gas phase diagram as a function of these two ``fields.''

DOI
10.1103/physrevb.33.7777

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We investigate the Fermi gas model for one-dimensional (1D) conductors as a function of chemical potential and of the applied magnetic field. The bosonization method allows to prove the equivalence between these parameters, the first acting on charge degrees of freedom, the second on spin degrees of freedom. A number of results available in the literature can thus be connected. We also use the mapping to the 2D classical Coulomb gas and a two-cutoff renormalization-group method, the two energy scales being the bandwidth and the Zeeman energy (or the chemical potential). We obtain a coherent description of the Fermi gas phase diagram as a function of these two ``fields.''
Several exact results are proved for two models of one-dimensional conductors, a model with transfer cutoff and spin- and charge-carrying interactions and the usual backscattering model with a bandwidth cutoff. A set of Ward identities is derived which connects the three-point charge vertex parts with single-particle Green's functions. These are combined with a modified renormalization-group scheme to prove the scale invariance of the couplings between charge densities in the absence of umklapp processes. The Ward identities are also used for the computation of the correlation functions in the charge sector of the system. Then some canonical transformations are introduced which allow one to relate various response functions among themselves. From these relations the phase boundaries of the ground state can be established. It is shown that the transfer cutoff and the backscattering models have the same phase diagram.
In this paper, the chemical potential of two-dimensional (2D) and quasi-one-dimensional (Q1D) multisubband charged Fermi gases is evaluated. We start with a rather general formula for the thermodynamic potential of an ideal quantum statistical system with arbitrary occupation-number to calculate, as a particular case, the chemical potential of the multisubband 2D Fermi gas described by a quadratic energy spectrum. The chemical potential is also studied in the case of a low-dimensional Fermi gas in the presence of a quantizing magnetic field. The same approach is used to study the chemical potential of a multisubband Q1D Fermi gas. The influence of temperature is considered. We found interesting analytical results for special limits as well as numerical results that may be important for the description of both the thermodynamic and kinetic properties of Fermi systems in low dimensionality.
For nearly a decade, quasi-one-dimensional conductors have been the subject of intensive study. Theoretically, much attention has been devoted to the development of one-dimensional Fermi gas models, some which may be solved exactly, and to the calculation of their response functions. After a review of this theory, a different approach is adopted in the investigation of two models. The dielectric response theory of the three-dimensional Coulomb gas has been applied to an anisotropic system in which the particles interact with an effective one-dimensional long-range potential. Within the framework of the approximation of Singwi, Tosi, Land, and Sjolander, the dielectric properties of the model are examined in order to determine the conditions under which it is unstable with respect to formation of a charge density wave state. It is found that the positive neutralizing background must be polarizable in order for such an instability to occur. The same approximation method, when applied to a one-dimensional fermion gas with a ʃ-function interaction may be compared with the exact solution of Yang. This solution, which exists in the form of coupled integral equations, has been calculated numerically, and, as predicted by the Lieb-Mattis theorem, the ground state is found to be non-magnetic. The approximation of Singwi et al. proves to give better correlation energies than other inexact methods, particularly at higher densities.
We have investigated the ground-state phase diagram of the one-dimensional Hubbard model with alternating chemical potentials at half-filling by bosonization technique and the Gaussian wave functional method. We calculate variations of the charge density wave (CDW) and the spin density wave (SDW) gaps, ad well as their classical trajectory c,s with increasing on-site Coulomb repoulsion potential. For the fixed potential, it is found that the transition from the band insulator (BI) to the spontaneously dimerized insulator (SDI) is of the Ising type, at which charge gap vanishes, while the transition from SDI to the Mott insulator (MI) is of the KT type.