Field-Induced Quantum Spin Nematic Liquid Phase in the S=1 Antiferromagnetic Heisenberg Chain with Additional Interactions

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. 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.
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 study, we investigate the S=1 antiferromagnetic chain with some additional interactions. The previous DMRG[6] and numerical diagonalization[7] analyses of the S=1 antiferromagnetic chain with the biquadratic interaction indicated that the spin nematic liquid phase appears in higher magnetic field region of the magnetization process. On the other hand, the numerical diagonalization study[8] on the S=1 antiferromagnetic chain with the single-ion anisotropy revealed that a similar two-magnon bound state appears in lower field region of the magnetization process. Thus it would be interesting to investigate the magnetization process of the S=1 antiferromagnetic chain with both of the biqudratic interaction and the single-ion anisotropy. We will present several phase diagrams of this model obtained by the numerical diagonalization analysis.

[1] T. Sakai, T. Tonegawa and K. Okamoto, Physica Status Solidi B 247, 583 (2010) .
[2] N. Buttgen, K. Nawa, T. Fujita, M. Hagiwara, P. Kuhns, A. Prokofiev, A. P. Reyes, L. E. Svistov, K. Yoshimura and M. Takigawa, Phys. Rev B 90, 134401 (2014) .
[3] T. Hikihara, T. Tonegawa, K. Okamoto and T. Sakai, J. Phys. Soc. Jpn. 86, 054709 (2017).
[4] T. Tonegawa, T. Hikihara, K. Okamoto, S. C. Furuya, and T. Sakai, J. Phys. So. Jpn. 87, 104002 (2018).
[5] T. Sakai, K. Okamoto and T. Tonegawa, Phys. Rev. B 100, 054407 (2019)
[6] S. R. Manmana, A. M. Lauchli, F. H. I. Essler and F. Mila, Phys. Rev. B 83, 184433 (2011).
[7] T. Sakai, AIP Advances 11, 015306 (2021).
[8] T. Sakai, Phys. Rev. B 58, 6268 (1998).