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arXiv:1812.06253 · Physical review. B./Physical review. B

Parity dependent phase diagrams in spin-cluster two-leg ladders

Zongsheng Zhou, Fuzhou Chen, Yin Zhong, Hong‐Gang Luo, Jize Zhao

Published May 24, 2019• 2 citations
arXivHTMLPDF

Abstract

Motivated by the recent experiment on ${\mathrm{K}}_{2}{\mathrm{Cu}}_{3}\mathrm{O}{\left({\mathrm{SO}}_{4}\right)}_{3}$, an edge-shared tetrahedral spin-cluster compound [M. Fujihala, T. Sugimoto, T. Tohyama, S. Mitsuda, R. A. Mole, D. H. Yu, S. Yano, Y. Inagaki, H. Morodomi, T. Kawae, H. Sagayama, R. Kumai, Y. Murakami, K. Tomiyasu, A. Matsuo, and K. Kindo, Phys. Rev. Lett. 120, 077201 (2018)], we investigate two-leg spin-cluster ladders with the plaquette number ${n}_{p}$ in each cluster up to 6 by the density-matrix renormalization-group method. We find that the phase diagrams of such ladders strongly depend on the parity of ${n}_{p}$. For even ${n}_{p}$, the phase diagrams have two phases; one is the Haldane phase, and the other is the cluster rung-singlet phase. For odd ${n}_{p}$, there are four phases, which are a cluster-singlet phase, a cluster rung-singlet phase, a Haldane phase, and an even Haldane phase. Moreover, in the latter case the region of the Haldane phase increases while that of the cluster-singlet phase and the even Haldane phase shrinks as ${n}_{p}$ increases. We thus conjecture that in the large ${n}_{p}$ limit the phase diagrams will become independent of ${n}_{p}$. By analyzing the ground-state energy and entanglement entropy we obtain the order of the phase transitions. In particular, for ${n}_{p}=1$ there is no phase transition between the even Haldane phase and the cluster rung-singlet phase while for other odd ${n}_{p}$ there is a first-order phase transition. Our paper provides comprehensive phase diagrams for these cluster-based models and may be helpful to understand experiments on related materials.

DOI
10.1103/physrevb.99.205143

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