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J-Physics International Conference on Multipole Physics and Related Phenomena

Spin Nematic Phase of the Quantum Spin Nanotube

Tôru Sakai

Published Feb 12, 2020• 0 citations
Publisher

Abstract

The S=1/2 three-leg quantum spin nanotube with the ring exchange interaction is investigated using the numerical exact diagonalization of finte-size clusters and finite-size scaling analysis.The previous study suggested that the ring exchange interaction induces the quantum phase transition from the spin gap phase to some new phase.The present work indicates that the new phase is the spin nematic Tomonaga-Luttinger liquid phase.

DOI
10.7566/jpscp.29.014004

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•Sep 28, 2017•0 citations
The S=1/2 three-leg quantum spin nanotube with the ring exchange interaction is investigated using the numerical exact diagonalization of finte-size clusters and finite-size scaling analysis.The previous study suggested that the ring exchange interaction induces the quantum phase transition from the spin gap phase to some new phase.The present work indicates that the new phase is the spin nematic Tomonaga-Luttinger liquid phase.
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.
We investigate the S = 1/2 three-leg spin tube, which is the simplest spin nanotube, using the density matrix renormalization group (DMRG) and the numerical exact diagonalization (ED), conbined with a finite-size scaling analysis. Particularly, we intruduce the lattice distortion from the regular triangle unit to the isosceles one. In our previous works, we revealed that the S = 1/2 isosceles triangle spin tube exhibits following exotic quantum phenomena: the quantum phase transition between the spin gapped and gapless spin liquid phases, the 1/3 magnetization plateau due to two different mechanisms, and a new phase between the two plateau phases where the translational symmetry is spontaneously broken. We briefly review these results and show our new calculation of the expectation value of the magnetization at each site to specify the spin structure in the new field induced phase.
Field-Induced Spin Nematic Phase in the S=1S=1S=1 Anisotropic Spin Ladder
The S=1 spin ladder with the easy-axis single-ion anisotropy is investigated using the numerical diagonalization and the finite-size scaling analysis. It is found that the field-induced nematic Tomonaga-Luttinger liquid phase appears above the critical field. In addition, there exists another critical field at which the quantum phase transition from the nematic Tomonaga-Luttinger liquid phase to the conventional field-induced Tomonaga- Luttinger liquid phase occurs. Besides some phase diagrams are presented.
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 (ED), combined with the recently developed level spectroscopy analysis. Particularly, we introduce the lattice distortion from the regular triangle unit to the isosceles one. We revealed that the S = 1/2 isosceles triangle spin tube exhibits the quantum phase transition between the spin gapped and gapless spin liquid phases.
The spin nematic phase, which is a kind of multipole phases, has attracted a lot of interest in the field of the strongly correlated electron systems, as well as the quantum spin liquid phase. Using the numerical exact diagonalization, the density matrix renormalization group (DMRG) calculation, and the finite-size scaling analysis, it is found that some spin nematic and spin liquid phases appear in the anisotropic and/or frustrated quantum spin systems. In our previous work, quasi-one-dimensional quantum spin systems with the easy-axis anisotropy in magnetic field are theoretically investigated using the numerical exact diagonalization, the density matrix renormalization group (DMRG) and the finite-size scaling analysis[1]. It was found that a field-induced nematic phase appears at some critical field in the anisotropic spin ladder and the mixed spin chain. The nematic phase is characterized by the power-law decay in the correlation function of the second-order spin moment. In addition at some higher critical field a quantum phase transition can occur to the conventional field-induced Tomonaga-Luttinger liquid. Several typical magnetization curves calculated by DMRG are presented. We will also propose an experiment to observe these field-induced transitions by NMR measurements. The field-induced incommensurate order observed in azurite, which is modeled by the distorted diamond chain, by the recent NMR measurement will be also discussed. Recently the field-induced nematic phase was observed on the frustrated spin ladder system[2,3]. So we study on a frustrated spin ladder system[4], using the numerical diagonalization and DMRG. As a result, it is found that several exotic quantum phases, including the spin-nematic liquid phase. We also report some exact eigen states of the present model. [1] T. Sakai, T. Tonegawa and K. Okamoto, Physica Status Solidi B 247 (2010) 583.[2] N. Buttgen et al., Phys. Rev B 90, (2014) 134401.[3] K. Nawa et al., J. Phys. Soc. Jpn., 82 (2013) 094709.[4] T. Hikihara, T. Tonegawa, K. Okamoto and T. Sakai, J. Phys. Soc. Jpn. 86 (2017) 054709.