Translational Symmetry Broken Magnetization Plateau of the One-Dimensional Quantum Spin Systems with Competing Anisotropies*

The magnetization plateau is one of interesing phenomena in the field of the condensed matter physics. It was proposed as the spin gap induced by the external magnetic field[1]. According to the rigorous theorem derived from the Lieb-Schultz-Mattis one, the necessary condition of the magnetization plateau is the relation Q(S-m)=integer, where S and m are the total spin and the magnetization per unit cell, respectively, and Q is the periodicity of the wave function. The numerical diagonalization of finite-size clusters and the size scaling analysis[2] indicated that the spin-3/2 antiferromagnetic chain with the single-ion anisotropy exhibits the 1/3 magnetization plateau with Q=1. In the case of the spin-1/2 ferromagnetic-antiferromagnetic bond-alternating chain, because of S=1, the translational symmetry should be broken for the appearance of the magnetization plateau with m=1/2. Now the competing coupling anisotropies are introduced to the ferromagnetic and antiferromagnetic bonds.The numerical diagonalization of finite-size clusters and the level spectroscopy analysis indicate that the 1/2 magnetization plateau would appear, if the easy-plane anisotropy at the ferromagnetic bond and the easy-axis one at the antiferromagnetic bond are sufficielntly large. The several phase diagram with respect to the two anisotropies at m=1/2, depending on the ratio of the ferromagnetic and antiferromagnetic coupling constants. The translational symmetry broken plateau based on a similar mechanism is predicted for the S=1 and S=2[3,4] antiferromagnetic chains with the single-ion anisotropy and the couplind anisotropy competing with each other. 

[1]M. Oshikawa, M. Yamanaka and I. Affleck, Phys. Rev. Lett. 78, 1984 (1997). 

[2]T. Sakai and M. Takahashi, Phys. Rev. B 57, R3201 (1998).

[3]T. Sakai, T. Yamada, R. Nakanishi, R. Furuchi, H. Nakano, H. Kaneyasu, K. Okamoto and T. Tonegawa, J. Phys. Soc. Jpn. 91, 074702 (2022).

[4]T. Yamada, R. Nakanishi, R. Furuchi, H. Nakano, H. Kaneyasu, K. Okamoto and T. Tonegawa, JPS Conf. Proc. 38, 011163 (2022).