N\'eel Ordered Magnetic Phases in Bipartite Quasicrystals

TL;DR

This study uses quantum Monte Carlo simulations to explore magnetic phases in bipartite quasicrystals, revealing the presence of Neel ordered states including antiferromagnetism, altermagnetism, and ferromagnetism, depending on symmetry properties.

Contribution

It introduces a symmetry-based criterion to classify Neel magnetic states in bipartite quasicrystals, supported by comprehensive numerical evidence.

Findings

Neel states in bipartite QCs can be AFM, AM, or FM.

Symmetry analysis determines the type of Neel order based on sublattice relations.

Examples include AM in Thue-Morse QCs and FM in Penrose QCs.

Abstract

Magnetism is a fundamental research area in which the recently proposed altermagnetism (AM) has become an emergent frontier. Very recently, the quasicrystal (QC) was proposed as a possible platform to realize AM. However, the existence of AM in QCs still lacks vigorous evidence. In this work, we adopt the sign-problem-free projector quantum Monte Carlo (PQMC) algorithm to investigate the magnetic phases in the half-filled Hubbard models in various 2D bipartite QCs, and always obtain N\'eel ordered states. While the N\'eel states in bipartite crystals are usually antiferromagnetism (AFM), we find it common that those in bipartite QCs can also be AM or ferromagnetism (FM). Based on symmetry analysis, combined with our comprehensive PQMC results, we propose a general criterion for determining the magnetism classes of the N\'eel states in a bipartite QC: According to whether the two sublattices are related by the inversion, the other point-group operation, or no operation about the unique symmetry center in the QC, the corresponding N\'eel state is AFM, AM or FM, respectively. For example, our results yield AM for the two $D_4$-symmetric Thue-Morse QCs and FM for the $D_5$-symmetric Penrose QC at half-filling. Our results provide a solid foundation for experimental investigations and potential applications of different classes of magnetism in QCs.