Insulator-to-insulator transition and sign problem in the periodic Anderson model with a staggered potential

Motivated by the recent proposal that the Monte Carlo sign problem might be used as an indicator of quantum phase transitions, we simulate the periodic Anderson model at half-filling with a staggered ionic potential using the determinant quantum Monte Carlo (DQMC) approach. We observe a phase transition from a band insulator to a Kondo insulator as the hybridization increases. At finite temperature, an intermediate metallic region emerges between two insulating phases, which is characterized by a pseudogap in the spectral functions near the boundary of the intermediate region and a quasiparticle peak in the middle. The latter coincides with a crossing point of the $f$-electron occupation on different sublattices as well as the maximum antiferromagnetic (AFM) correlations. The metallic region extrapolates to a single quantum critical point at zero temperature, which may result in exotic quasiparticle excitations associated with the emergent metallic state. The Monte Carlo sign problem is found to be most pronounced in the quantum critical region, implying a close connection between the two phenomena. Our results are qualitatively supported by the Hartree-Fock (HF) mean-field calculations. Our work reveals interesting physics in inhomogeneous Kondo lattice systems that may be worthwhile of more investigations in the future.