Ground-state phase diagram of S = 1/2 Heisenberg model on 2D square-hexagon-octagon lattice

TL;DR

This study maps the ground-state phase diagram of the S=1/2 Heisenberg model on a 2D square-hexagon-octagon lattice, revealing five phases including a topologically protected Haldane-like phase, using advanced quantum Monte Carlo and DMRG methods.

Contribution

It provides the first detailed phase diagram of the Heisenberg model on the SHO lattice, identifying a novel Haldane-like SPT phase and characterizing phase transitions.

Findings

Identified five distinct ground-state phases including a topological SPT phase.

Confirmed the topological nature via degeneracy of ground states and entanglement spectrum.

Determined phase boundaries and universality class of transitions.

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 $0<\lambda_1=J_2/J_1<4, 0<\lambda_2=J_3/J_1<4$: a N\'eel 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.