Correlated electron systems on the Apollonian network

Abstract

Strongly correlated electrons on an Apollonian network are studied using the Hubbard model. Ground-state and thermodynamic properties, including specific heat, magnetic susceptibility, spin-spin correlation function, double occupancy, and one-electron transfer, are evaluated applying direct diagonalization and quantum Monte Carlo techniques. In the strong-coupling limit, the quantum anisotropic spin-1∕2 Heisenberg model is used and the phase diagram is discussed using the renormalization group method. The results support an antiferromagnetic order with a metal-insulator transition for U∕t=11.1 at temperature T=0 and a tendency toward a nonordered phase in the half-filled Hubbard model for any U∕t. We also indicate that the spectral dimension must control the magnetic behavior on the Apollonian network.