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We describe here a quantum simulator of extended bipartite Hubbard model withbroken sublattice symmetry. The simulator consists of a structured lateral gateconfining two dimensional electrons in a quantum well into artificial minimaarranged in a hexagonal lattice. The sublattice symmetry breaking is generatedby forming an artificial triangular graphene quantum dot (ATGQD) with zigzagedges. The resulting extended Hubbard model generates tunable ratio oftunneling strength to electron-electron interactions and of sublattice symmetrywith control over shape. The validity of the simulator is confirmed for smallsystems using mean-field and exact diagonalization many-body approaches whichshow that the ground state changes from a metallic to an antiferromagnetic (AF)phase by varying the distance between sites or depth of the confiningpotential. The one-electron spectrum of these triangular dots contains amacroscopically degenerate shell at the Fermi level. The shell persists at themean-field level for weak interactions (metallic phase) but disappears forstrong interactions, in the AF phase. We determine the effects ofelectron-electron interactions on the ground state, the total spin, and theexcitation spectrum as a function of filling of the ATGQD. We find that thehalf-filled charge neutral shell leads to a partially spin polarized state inboth metallic and AF regimes in accordance with Liebs theorem. In both regimesa relatively large gap separates the spin polarized ground state to the firstexcited many-body state at half filling of the degenerate shell. By adding orremoving an electron, this gap drops dramatically, and alternate total spinstates emerge with energies nearly degenerate to a spin polarized ground state.

Quantum simulator of extended bipartite Hubbard model with broken sublattice symmetry: magnetism, correlations, and phase transitions