Ground state phase diagram and Haldane-like symmetry-protected phase in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mm

Using stochastic series expansion quantum Monte Carlo method and density matrix renormalization group, we study the ground-state phase diagram of $S=1/2$ Heisenberg model on 2D square-hexagon-octagon (SHO) lattice. In this model, we consider two kinds of nearest-neighbor interaction (intra-hexagon interaction $J_1$ and inter-hexagon $J_2$) and the selected third nearest-neighbor interaction $J_3$ along $x$ direction. From our calculations, there are five phases in the parameters regime $0<λ_1=J_2/J_1<4, 0<λ_2=J_3/J_1<4$, including a Néel antiferromagentic phase, a Haldane-like symmetry protected topological phase, a hexagon phase and two dimer phases. In the Haldane-like SPT phase, we characterized its topological nature using the degeneracy of ground-state energy under open boundary condition and the entanglement spectrum. To characterize the phase boundaries, we use spin stiffness and Binder cumulant to do the comprehensive finite-size scalings. From data collapse, the critical behaviors of all the nonmagnetic phases to the antiferromagnetic phase belong to the 3D $O(3)$ Heisenberg universality class. As a theoretical exploration, our work establishes a foundational framework for understanding 2D magnetism on the SHO lattice.