Quantum phase transitions of the asymmetric three-leg spin tube

TL;DR

This paper explores quantum phase transitions in an asymmetric three-leg spin tube, revealing a narrow gapped region and confirming the phase diagram's accuracy through numerical methods and effective theories.

Contribution

It introduces an effective theory for the asymmetric spin tube and validates the global phase diagram with numerical analyses, clarifying the nature of phase transitions.

Findings

Finite spin gap appears near the rung-symmetric line.

The phase diagram is qualitatively correct according to numerical data.

Transitions are in the Berezinskii-Kosterlitz-Thouless universality class.

Abstract

We investigate quantum phase transitions of the S=1/2 three-leg antiferromagnetic spin tube with asymmetric inter-chain (rung) exchange interactions. On the basis of the electron tube system, we propose a useful effective theory to give the global phase diagram of the asymmetric spin tube. In addition, using other effective theories we raise the reliability of the phase diagram. The density-matrix renormalization-group and the numerical diagonalization analyses show that the finite spin gap appears in a narrow region around the rung-symmetric line, in contrast to a recent paper by Nishimoto and Arikawa [Phys. Rev. B78, 054421 (2008)]. The numerical calculations indicate that this global phase diagram obtained by use of the effective theories is qualitatively correct. In the gapless phase on the phase diagram, the numerical data are fitted by a finite-size scaling in the c=1 conformal field theory. We argue that all the phase transitions between the gapful and gapless phases belong to the Berezinskii-Kosterlitz-Thouless universality class.