Correlated electrons systems on the Apollonian network

TL;DR

This paper investigates the properties of strongly correlated electrons on an Apollonian network using the Hubbard model, revealing various magnetic behaviors and phase diagrams through numerical and analytical methods.

Contribution

It applies the Hubbard model and quantum Monte Carlo techniques to analyze electron correlations on the Apollonian network, providing new insights into magnetic phases and phase transitions.

Findings

Long-range magnetic order in ferromagnetic coupling

Paramagnetic phase in antiferromagnetic coupling at finite temperatures

Phase diagram analysis using renormalization group methods

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. The results support several types of magnetic behavior. 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. For ferromagnetic coupling, we always observe the existence of long-range order. For antiferromagnetic coupling, we find a paramagnetic phase for all finite temperatures.