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arXiv:2510.23376 · Physical review. B./Physical review. B

Ground state phase diagram and Haldane-like symmetry-protected phase in the S = 1 2 Heisenberg model on the two-dimensional square-hexagon-octagon lattice

Yumeng Luo, Yuehong Li, Mengfan Jiang, Muwei Wu, Jian-Jian Yang, Dao‐Xin Yao, Han-Qing Wu

Published Dec 11, 2025• 2 citations
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Abstract

Using stochastic series expansion quantum Monte Carlo and density matrix renormalization group methods, we investigate the ground-state phase diagram of the $S=1/2$ Heisenberg model on the two-dimensional square-hexagon-octagon (SHO) lattice. The model incorporates nearest-neighbor interactions $J_1$ (intrahexagon interaction) and $J_2$ (interhexagon), as well as a selected third-neighbor interaction $J_3$ along the $x$ direction. We identify five distinct phases in the parameter regime $0<λ_1=J_2/J_1<4, 0<λ_2=J_3/J_1<4$: a Néel antiferromagentic phase, two dimer phases (orthogonal and ladder staggered dimers), a hexagon singlet phase, and notably a Haldane-like symmetry-protected topological (SPT) phase. The topological nature of the Haldane-like phase is confirmed by the degeneracy of the ground-state energy under open boundary conditions and the twofold degeneracy of the entanglement spectrum. Phase boundaries are accurately determined using finite-size scaling of the spin stiffness and Binder cumulant. Data collapse analysis reveals that all transitions from nonmagnetic phases to the antiferromagnetic phase belong to the three-dimensional $O(3)$ Heisenberg universality class. In addition, we investigate the robustness of the SPT phase to other interactions, such as those that could arise in experimental materials. Our work establishes a comprehensive theoretical framework for understanding magnetic and topological phases on the SHO lattice.

DOI
10.1103/ycsq-w3fr

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The S=1/2S=1/2S=1/2 and S=1S=1S=1 two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for S=1,S=1,S=1, we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended-parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchain-coupling, case.
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