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Employing the projective formalism of determinant quantum Monte Carlo (DQMC)simulations, we meticulously explore the ground-state phase diagram andcritical behavior of the half-filled Hubbard model on a square-hexagon-octagon(SHO) lattice. This lattice, a two-dimensional (2D) structure comprisingsquares, hexagons, and octagons, is representative of the biphenylene network(BPN). Our findings reveal an intriguing ground-state phase diagram, featuringan antiferromagnetic (AFM) Mott insulating phase enveloped by threevalence-bond solid-like (VBS-like) insulating phases. Analyzing thesingle-particle gap, spin gap, and single-particle spectral function, weobserve that the metallic state in the noninteracting case becomes unstableunder the influence of Hubbard U. This interaction drives the system into ahexagon insulating phase before transitioning into an AFM Mott insulatingphase. To quantify the critical exponents, we use finite-size scalingtechniques. The critical exponents of quantum critical points between the AFMMott insulating phase and two insulating phases, plaquette insulator andethylene insulator, closely align with the 3D O(3) universality class. However,the critical exponents of quantum critical points between the hexagoninsulating phase and the AFM Mott insulating phase deviate from the 3D O(3)universality class. This deviation is a finite-size effect and can beattributed to the coupling between the fluctuations of magnetic order parameterand very low-energy fermionic excitations. Our comprehensive study not onlyadvances the understanding of correlation effects on the SHO lattice but alsosheds light on the less-explored critical exponents in weakly insulatingquantum critical point.

Phase diagram and critical behavior of Hubbard model on the square-hexagon-octagon lattice