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).