Quantum phase transitions from competing short- and long-range interactions on a $π$-flux lattice

Quantum phase transitions from the cluster-charge interaction, which is composed of competing short- and long-range interactions, are investigated on a $π$-flux lattice by using the mean-field theory and determinant quantum Monte Carlo (DQMC) simulations. Both methods identify a plaquette-dimer phase, which develops from a finite interaction strength. While its signature in DQMC is relatively weak, a obvious antiferromagnetic transition is revealed in the spin structure factor instead. The corresponding critical interaction and exponents are readily obtained by finite-size scalings, with the plaquette-dimer structure factor that can also be well scaled. These results suggest a possible deconfined quantum critical point between the plaquette-dimer and antiferromagnetic phases driven by the cluster-charge interaction on a $π$-flux lattice.

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