We study the S = 1/2 Heisenberg antiferromagnet on the floret pentagonal lattice by numerical diagonalization method. This system shows various behaviours that are different from that of the Cairo-pentagonal-lattice antiferromagnet. The ground-state energy without magnetic field and the magnetization process of this system are reported. Magnetization plateaux appear at one-ninth height of the saturation magnetization, at one-third height, and at seven-ninth height. The magnetization plateaux at one-third and seven-ninth heights come from interactions linking the sixfold-coordinated spin sites. A magnetization jump appears from the plateau at one-ninth height to the plateau at one-third height. Another magnetization jump is observed between the heights corresponding to the one-third and seven-ninth plateaux; however the jump is away from the two plateaux, namely, the jump is not accompanied with any magnetization plateaux. The jump is a peculiar phenomenon that has not been reported.

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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.

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The S = 1/2 Heisenberg antiferromagnet on the floret-pentagonal lattice with two kinds of interaction strength is studied by the numerical-diagonalization method. It is known that, near the five-ninth of the saturation magnetization, this system shows a magnetization jump that is not accompanied by magnetization plateaux. We focus our attention on the behavior of this system around the five-ninth of the saturation magnetization; the changes of the magnetization jump and plateau at and around this magnetization are clarified from the diagonalization data for finite-size systems up to 45 sites.

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The magnetization process of the S=1/2S=1/2 delta chain with the anisotropic ferromagnetic interaction is investigated using the numerical diagonalization of finite-size clusters. It is found that the spin nematic liquid phase appears in higher magnetization region, as well as the SDW liquid one in lower region.

We report an inconsistent way of plotting in a figure in Furuchi R, Nakano H, Todoroki N and Sakai T (2021 J. Phys. Commun. 5 125 008) and present a consistent figure. This replacement does not change the main conclusions in Furuchi R, Nakano H, Todoroki N and Sakai T (2021 J. Phys. Commun. 5 125 008).