Magnetic order and novel quantum criticality in the strongly interacting quasicrystals

TL;DR

This study uses sign-problem-free quantum Monte Carlo simulations to explore how aperiodic geometries in two-dimensional quasicrystals influence magnetic quantum criticality, revealing a new universality class driven by geometry and correlations.

Contribution

It demonstrates that specific aperiodic geometries fundamentally alter quantum critical behavior, identifying a novel universality class in 2D quasicrystals with unique critical exponents.

Findings

Penrose tiling induces magnetic order at infinitesimal interactions.

Thue-Morse lattice requires finite interaction for magnetic transition.

Identified a quantum critical point with unconventional critical exponents.

Abstract

We present the sign-problem-free quantum Monte Carlo study of the half-filled Hubbard model on two-dimensional quasicrystals, revealing how specific aperiodic geometries fundamentally dictate quantum criticality. By comparing the Penrose and Thue-Morse quasicrystals, we demonstrate that the nature of the magnetic phase transition is controlled by the electronic density of states (DOS): while the singular DOS of the Penrose tiling induces magnetic order at infinitesimal interaction strengths, the Thue-Morse lattice requires a finite critical interaction to drive the transition. Crucially, through a novel boundary construction strategy and rigorous finite-size scaling, we identify a quantum critical point on the Thue-Morse quasicrystal with critical exponents ($\nu \approx 0.94$, $\beta \approx 0.72$ and $z\approx 1.51$) that deviate significantly from the conventional $(2+1)$D Heisenberg $O(3)$ class. These findings establish the existence of a novel universality class driven by the interplay between electronic correlations and aperiodic geometry, challenging standard paradigms of magnetic criticality in two dimensions.