Entanglement Entropy in the Bilayer Hubbard Model on the Bethe Lattice

초록

Using dynamical mean field theory (DMFT) in combination with a continuous-time quantum Monte Carlo (DMFT+CTQMC) tool, we studied the von Neumann entanglement entropy (5) in a bilayer Hubbard model on the Bethe lattice. Jump behaviors in S are observed at the critical points among the Fermi liquid, the Mott insulator, and the band insulator at a low temperature, similar to the results in a double occupancy which the DMFT+CTQMC method can easily calculate. As novel results that the double occupancy cannot account for, the behaviors of S in the weak region with metallic states can supply information on the coherence temperature and the Fermi temperature without the need to analyze the transport properties through analytical continuation of the self-energy or differentiation of the energy. In addition, when the strength of the interlayer hopping is tuned in the strong interaction region, S increases in the Mott phase owing to the short-range spatial fluctuations between impurities of bilayers while it decreases in the band phase. These behaviors mean that S might provide a criterion for separation between the Mott insulator and the band insulator as an order parameter in the strong interaction region.