Antiferromagnetic order in the Hubbard Model on the Penrose Lattice

TL;DR

This study investigates antiferromagnetic order in the Hubbard model on a quasiperiodic Penrose lattice, revealing unique spatial magnetization patterns influenced by lattice structure and Coulomb interaction strength.

Contribution

It provides the first detailed analysis of antiferromagnetic order in the Hubbard model on a quasiperiodic lattice, highlighting the effects of lattice structure and interaction strength on magnetic patterns.

Findings

Finite staggered magnetizations at infinitesimal U due to localized states

Magnetization patterns reflect quasiperiodic structure and evolve with U

Mode analysis reveals pattern changes in perpendicular space

Abstract

We study an antiferromagnetic order in the ground state of the half-filled Hubbard model on the Penrose lattice and investigate the effects of quasiperiodic lattice structure. In the limit of infinitesimal Coulomb repulsion $U \rightarrow +0$, the staggered magnetizations persist to be finite, and their values are determined by confined states, which are strictly localized with thermodynamics degeneracy. The magnetizations exhibit an exotic spatial pattern, and have the same sign in each of cluster regions, the size of which ranges from 31 sites to infinity. With increasing $U$, they continuously evolve to those of the corresponding spin model in the $U=\infty$ limit. In both limits of $U$, local magnetizations exhibit a fairly intricate spatial pattern that reflects the quasiperiodic structure, but the pattern differs between the two limits. We have analyzed this pattern change by a mode analysis by the singular value decomposition method for the fractal-like magnetization pattern projected into the perpendicular space.