Numerical Study on Quantum Phase Transitions of the Spin Tubes

We investigate quantum phase transitions of the $S=\frac{1}{2}$ three-leg antiferromagnetic spin tube with asymmetric interchain (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. B 78, 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.We investigate quantum phase transitions of the $S=\frac{1}{2}$ three-leg antiferromagnetic spin tube with asymmetric interchain (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. B 78, 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.

arXiv:0807.4769Physical Review BNov 17, 200856 citations

Quantum Phase Transition of the Twisted Spin Tube

Yuta Tachibana, Yuki Ueno, Tomosuke Zenda +2 more

The $S=1/2$ twisted three-leg spin tube with the lattice distortion from the regular triangle to the isosceles one is investigated using the numerical diagonalization of finite-size clusters and the phenomenological renormalization group analysis. It is found that the quantum phase transition occurs from the spin gap phase to another one with respect to this lattice distortion.The $S=1/2$ twisted three-leg spin tube with the lattice distortion from the regular triangle to the isosceles one is investigated using the numerical diagonalization of finite-size clusters and the phenomenological renormalization group analysis. It is found that the quantum phase transition occurs from the spin gap phase to another one with respect to this lattice distortion.

arXiv:1910.02587International Conference on Strongly Correlated Electron Systems (SCES)Mar 18, 20200 citations

On the phase transitions in quantum spin systems

R. Micnas, K. A. Chao

Physics Letters AJul 1, 19853 citations

Exotic Quantum Phase Transitions in Spin Nanotubes

Tôru Sakai, Masahiro Sato, Kouichi Okunishi +2 more

Recently some quantum spin systems on tube lattices, so called spin nanotubes, have been synthesized. They are expected to be interesting low-dimensional systems like the carbon nanotubes. As the first step of theoretical study on the spin nanotube, we investigate the S=1/2 three-leg spin tube, which is the simplest one, using the numerical exact diagonalization and the finite-size scaling analysis. In our previous works the quantum phase transition between the spin-gap and gapless phases was revealed to occur due to the asymmetric lattice distortion. In addition the transition between the magnetization plateau and gapless phases at 1/3 of the saturation magnetization induced by the same distortion. Recently we found that the Tomonaga-Luttinger liquid is realized in the 1/3 magnetization plateau phase for the symmetric three-leg spin tube.Recently some quantum spin systems on tube lattices, so called spin nanotubes, have been synthesized. They are expected to be interesting low-dimensional systems like the carbon nanotubes. As the first step of theoretical study on the spin nanotube, we investigate the S=1/2 three-leg spin tube, which is the simplest one, using the numerical exact diagonalization and the finite-size scaling analysis. In our previous works the quantum phase transition between the spin-gap and gapless phases was revealed to occur due to the asymmetric lattice distortion. In addition the transition between the magnetization plateau and gapless phases at 1/3 of the saturation magnetization induced by the same distortion. Recently we found that the Tomonaga-Luttinger liquid is realized in the 1/3 magnetization plateau phase for the symmetric three-leg spin tube.

Journal of Physics Conference SeriesDec 17, 20121 citation

We investigate quantum phase transitions of the

S=\frac{1}{2}

three-leg antiferromagnetic spin tube with asymmetric interchain (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. B 78, 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.

The

S=1/2

twisted three-leg spin tube with the lattice distortion from the regular triangle to the isosceles one is investigated using the numerical diagonalization of finite-size clusters and the phenomenological renormalization group analysis. It is found that the quantum phase transition occurs from the spin gap phase to another one with respect to this lattice distortion.