Site-selective correlations in strongly-interacting quasicrystals

Quasicrystals provide an interesting framework to study interacting flat-band systems, due to the existence of a geometrically-enforced macroscopic number of zero-energy states. Here, we present quantum Monte Carlo (QMC) simulations of the Hubbard model on quasicrystals with different types of tilling. We investigate the behavior of the imaginary time Green’s functions G(i,τ=β/2), which acts as a proxy of the local spectral function A_z(ω), on sites (orbitals) with different coordination number z. A "site-selective" behavior is found, where data for G(i,τ=β/2) for sites i with different z exhibit a crossing point T* as the temperature T is varied. By tracking T* as a function of the Hubbard interaction U, which controls the quantum critical behavior, the quantum phase transition can be located by identifying the value of U* for which T*(U) → 0. We compare the estimated U* directly with the U_c value extracted from the behavior of the specific heat C(T) for different types of quasicrystals.