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arXiv:2208.10988 · International Conference on Low Temperature Physics (LT)

Nematic Tomonaga–Luttinger Liquid Phase in an S = 1/2 Ferromagnetic–Antiferromagnetic Bond-Alternating Chain

Takashi Tonegawa, Kiyomi Okamoto, K. Nomura, Tôru Sakai

Published May 22, 2023• 1 citation
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Abstract

We numerically investigate the ground-state phase diagram of the S = 1/2 ferromagneticantiferromagnetic bond-alternating chain, in which the ferromagnetic interactions are stronger than the antiferromagnetic ones, and the anisotropies of the former and latter interactions are of the Ising-type and the XY-type, respectively.We use various numerical methods, such as the level spectroscopy and phenomenological renormalization-group analyses of the numerical data obtained by the exact diagonalization method, and so on.The resultant phase diagrams contain the ferromagnetic, XY1, singlet-dimer, and up-up-down-down phases as well as the nematic Tomonaga-Luttinger liquid (nTLL) phase which appears in a wide region of the interaction parameters.Perturbation calculations from the strong limit of the ferromagnetic interactions reproduce fairly well the numerical results of the phase boundary lines associated with the nTLL phase in the phase diagrams.

DOI
10.7566/jpscp.38.011154

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By using mainly numerical methods, we investigate the ground-state phase diagram (GSPD) of an S=1S=1S=1 ferromagnetic-antiferromagnetic bond-alternating chain with the XXZXXZXXZ and the on-site anisotropies. This system can be mapped onto an anisotropic spin-2 chain when the ferromagnetic interaction is much stronger than the antiferromagnetic interaction. Since there are many quantum parameters in this system, we numerically obtained the GSPD on the plane of the magnitude of the antiferromagnetic coupling versus its XXZXXZXXZ anisotropy, by use of the exact diagonalization, the level spectroscopy as well as the phenomenological renormalization group. The obtained GSPD consists of six phases. They are the $XY1,thelarge−1, the large-1,thelarge−D$ (LD), the intermediate-DDD (ID), the Haldane (H), the spin-1 singlet dimer (SD), and the Néel phases. Among them, the LD, the H, and the SD phases are the trivial phases, while the ID phase is the symmetry-protected topological phase. The former three are smoothly connected without any quantum phase transitions. It is also emphasized that the ID phase appears in a wider region compared with the case of the GSPD of the anisotropic spin-2 chain with the XXZXXZXXZ and the on-site anisotropies. We also compare the obtained GSPD with the result of the perturbation theory.
The magnetization process of the S = 1 antiferromagnetic chain with the single-ion anisotropy D and the biquadratic interaction is investigated using the numerical diagonalization.Both interactions stabilize the 2-magnon Tomonaga-Luttinger liquid (TLL) phase in the magnetization process. Based on several excitation gaps calculated by the numerical diagonalization, some phase diagrams of the magnetization process are presented. These phase diagrams reveal that the spin nematic dominant TLL phase appears at higher magnetizations for sufficiently large negative D.
Abstract The magnetization process of the S = 1 antiferromagnetic chain with the single-ion anisotropy D and the biquadratic interaction is investigated using the numerical diagonalization. Both interactions stabilize the 2-magnon Tomonaga-Luttinger liquid (TLL) phase in the magnetization process. Based on several excitation gaps calculated by the numerical diagonalization, some phase diagrams of the magnetization process are presented. These phase diagrams reveal that the spin nematic dominant TLL phase appears at higher magnetizations for sufficiently large negative D.
The ground state of the ferromagnetic-antiferromagnetic alternating spin-1/2 Heisenberg chain is studied with Ising-type anisotropy on the ferromagnetic bond. This model tends to the spin-1 antiferromagnetic Heisenberg chain with on-site anisotropy in the limit of strong ferromagnetic bond. It is found that the Haldane-gap phase, the large-D phase, and the two types of N\'eel phases appear as the ground state of this model. The duality relations between these four phases are proved for several limiting cases. The string order parameter characterizing the large-D phase is introduced based on these duality relations. The ground-state phase diagram is determined by the numerical diagonalization of the finite-size system.
The magnetization process of the S = 1/2 Kondo necklace spin chain with the anisotropic ferromagnetic interaction is investigated using the numerical diagonalization of finite-size systems. As a result, it is found that the two-magnon bound state appears in the field-induced Tomonaga-Luttinger liquid phase for sufficiently large anisotropy. The critical exponent analysis indicates that the spin nematic correlation is dominant at higher magnetization region in the two-magnon bound phase. The phase diagram with respect to the anisotropy and the magnetization is presented.