Spin-gap phases in Tomonaga-Luttinger liquids

Masaaki Nakamura, Atsuhiro Kitazawa, Kiyohide Nomura

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


We give details of the analysis of critical properties of spin-gap phases in one-dimensional lattice electron models. In 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 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.

Original languageEnglish
Pages (from-to)7850-7862
Number of pages13
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number11
Publication statusPublished - 1999

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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