Quantum Spin Nematic Liquid in the S=1 Antiferromagnetic Chain with the Biquadratic Interaction

Abstract

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 are induced by external magnetic field in the anisotropic and frustrated quantum spin systems. In our previous work[1], it was found that a field-induced nematic phase appears at some critical field in the anisotropic spin ladder. 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. Recently the field-induced nematic phase was observed on the frustrated spin ladder system[2]. So we studied on a frustrated spin ladder system[3], using the numerical diagonalization and DMRG. As a result, it was found that several exotic quantum phases, including the spin-nematic liquid phase. We also reported several interesting phase diagrams of this model and some related systems[4,5]. In the present paper, we investigate the S=1 antiferromagnetic chain with the biqadratic interaction, as another candidate that exhibits the field-induced spin nematic liquid pahse. The numerical diagonalization study of finite-size clusters indicates that the spin nematic liquid pahse appears in this model under sufficiently strong magnetic field. The phase diagram in the plane of the magnetic field and the biquadratic interaction is presented.