Spin-Gap Phases in Tomonaga-Luttinger Liquids

Details Spin-Gap Phases in Tomonaga-Luttinger Liquids Spin-Gap Phases in Tomonaga-Luttinger Liquids

1999-04-27

arxiv.org/abs/cond-mat/9904381v1

Phys. Rev. B 60 (1999) 7850

Physics

Condensed Matter

Strongly Correlated Electrons

14 pages(REVTeX), 9 figures(EPS), 1 table, To appear in PRB, Detailed paper of PRL 79 (1997) 3214 and JPSJ 67 (1998) 717

Scientific paper

10.1103/PhysRevB.60.7850

We give the details of the analysis for critical properties of spin-gap phases in one-dimensional lattice electron models. In the Tomonaga-Luttinger (TL) liquid theory, the spin-gap instability occurs when the backward scattering changes from repulsive to attractive. This transition point is shown to be equivalent to that of the level-crossing of the singlet and the triplet excitation spectra, using the c=1 conformal field theory and the renormalization group. Based on this notion, the transition point between the TL liquid and the spin-gap phases can be determined with high-accuracy from the numerical data of finite-size clusters. We also discuss the boundary conditions and discrete symmetries to extract these excitation spectra. This technique is applied to the extended Hubbard model, the t-J model, and the t-J-J' model, and their phase diagrams are obtained. We also discuss the relation between our results and analytical solutions in weak-coupling and low-density limits.

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