Progress of Theoretical Physics

Scaling Properties of One Dimensional Fermi Gas with Spin-Dependent Forward Scattering

T. Sugiyama

Published Aug 1, 1980• 5 citations

Abstract

In a one dimensional Fermi gas, the scaling properties of the model in which g2// is separated from g2⊥ are investigated. The Lie equations for the BGD model (that consists of backward and forward scatterings) are considered in the four independent invariant couplings, g1//*, g1⊥*, g2//* and g2⊥*, and the scaling trajectory is given in (g1//, |g1⊥|) plane. Further a phase diagram at 0K is investigated. Also a model with the Umklapp processes is considered.

DOI: 10.1143/ptp.64.406

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Progress of Theoretical Physics

Scaling Properties of One Dimensional Fermi Gas with Spin-Dependent Forward Scattering

T. Sugiyama

Published Aug 1, 1980• 5 citations

Publisher

Abstract

In a one dimensional Fermi gas, the scaling properties of the model in which g2// is separated from g2⊥ are investigated. The Lie equations for the BGD model (that consists of backward and forward scatterings) are considered in the four independent invariant couplings, g1//, g1⊥, g2//* and g2⊥*, and the scaling trajectory is given in (g1//, |g1⊥|) plane. Further a phase diagram at 0K is investigated. Also a model with the Umklapp processes is considered.

DOI: 10.1143/ptp.64.406

Related papers

On the Ground State of the Spin Dependent BGD Model

T. Sugiyama

Progress of Theoretical PhysicsMar 1, 19813 citations

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T. Sugiyama

Phase transitions of a quasi-one-dimensional Fermi gas are studied by the use of the renormalization group method for the fermion system without the bosonization. Intrachain backward and forward scatterings, pair electron hopping between different chains and exchange scattering of electrons in different chains are taken account of. Pair electron hopping gives rise to the singlet and triplet superconductor phase transitions. Electron exchange scattering gives rise to the spin density wave and charge density wave transitions. Calculation is made by the use of the one-dimensional dispersion. Following Menyhárd's method (Ref. 1) for the model with interchain backward scattering only, the change of the fluctuation from the one-dimensional region to the three-dimensional region is described. The transition temperatures are given by the bare couplings at high temperatures.Phase transitions of a quasi-one-dimensional Fermi gas are studied by the use of the renormalization group method for the fermion system without the bosonization. Intrachain backward and forward scatterings, pair electron hopping between different chains and exchange scattering of electrons in different chains are taken account of. Pair electron hopping gives rise to the singlet and triplet superconductor phase transitions. Electron exchange scattering gives rise to the spin density wave and charge density wave transitions. Calculation is made by the use of the one-dimensional dispersion. Following Menyhárd's method (Ref. 1) for the model with interchain backward scattering only, the change of the fluctuation from the one-dimensional region to the three-dimensional region is described. The transition temperatures are given by the bare couplings at high temperatures.

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Renormalization group for one-dimensional Fermi systems: Three-loop scaling equations

Edward H. Rezayi, Josef Sak, S. Talukdar

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Physical review. B, Condensed matterMay 1, 197912 citations

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Physical Review LettersSep 2, 1974749 citations

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Renormalization group for one-dimensional Fermi systems with long-range potential, exchange and umklapp interactions

Edward H. Rezayi, Josef Sak, Jenő Sólyom

Physical review. B, Condensed matterAug 1, 19797 citations

The one-dimensional Fermi system with Tomonaga-type (

{g}_{2}

) and back-scattering (

{g}_{1}

) interactions is studied by a weak-coupling renormalization-group method at the three-loop level. When the transfer cutoff procedure is used, the Gell-Mann-Low function for

{g}_{1}

depends on

{g}_{1}

alone, $\frac{d{g}_{1}}{d\ensuremath{\xi}}={{g}_{1}}^{2}+\frac{1}{2}{{g}_{1}}^{3}+\frac{1}{8}{{g}_{1}}^{4}$. Further, in the absence of umklapp processes the combination ${g}_{1}\ensuremath{-}2{g}_{2}$ is a scale invariant. These conclusions agree with the results of Luther and Emery derived by the boson representation method. Some novel calculational techniques for the derivation of the scaling equations are described and compared to the conventional scheme.