Spin-Gap Phases in Tomonaga-Luttinger Liquids
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/9904381,
title = {Spin-Gap Phases in Tomonaga-Luttinger Liquids},
author = {Masaaki Nakamura and Atsuhiro Kitazawa and Kiyohide Nomura},
journal= {arXiv preprint arXiv:cond-mat/9904381},
year = {2009}
}
Comments
14 pages(REVTeX), 9 figures(EPS), 1 table, To appear in PRB, Detailed paper of PRL 79 (1997) 3214 and JPSJ 67 (1998) 717