Spin-Gap Phases in Tomonaga-Luttinger Liquids

TL;DR

This paper analyzes the critical properties of spin-gap phases in one-dimensional electron models, using conformal field theory and numerical methods to accurately determine phase transition points.

Contribution

It introduces a high-precision method to identify spin-gap transition points via level-crossing analysis in finite-size numerical data.

Findings

Phase diagrams for extended Hubbard, t-J, and t-J-J' models are obtained.

Transition points between TL liquid and spin-gap phases are accurately determined.

The method relates numerical results to analytical solutions in specific limits.

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.