Néel Ordered Magnetic Phases in Bipartite Quasicrystals

TL;DR

Addressing whether altermagnetism can emerge in quasicrystals, the paper analyzes Néel ordering in half-filled Hubbard models on 2D bipartite QCs using sign-problem-free projector quantum Monte Carlo (PQMC). It introduces a symmetry-based criterion linking Néel order classes ($AFM$, $AM$, $FM$) to how the two sublattices transform under the QC’s point-group operations around a single symmetry center, and validates it with PQMC simulations across $D_4$-symmetric Thue-Morse, $D_2$-symmetric Thue-Morse, $D_5$ Penrose, and $D_8$ Ammann-Beenker lattices. PQMC results reveal robust AFM, AM, and FM Néel orders, with characteristic spin-resolved spectra distinguishing each class, thereby providing a solid theoretical foundation for experimental realization in QCs. The work also outlines future directions, including exploring varying $U$ and doping to access weak-coupling magnetism and potential unconventional superconductivity mediated by AM/FM fluctuations.

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 Néel ordered states. While the Néel 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 Néel 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 Néel 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.

Figures (11)

• Figure 1: Schematic diagrams of the lattice geometry-based criterion for determining the magnetic classes of Néel ordered states in bipartite QCs. (a) Néel ordered AFM is allowed in, e.g. the $D_2$-symmetric Thue-Morse QC, whose two sublattices are related by $\mathcal{P}$. A pair of sites related by $\mathcal{P}$ (dashed line) with opposite magnetic moments (red up arrow for spin-up and blue down arrow for spin-down) are marked in (a). (b) Néel ordered AM emerges in, e.g. the $D_4$-symmetric Thue-Morse QC, where other symmetry operation (e.g., the mirror $\sigma$) instead of $\mathcal{P}$ connects the two sublattices. The dashed line represents a mirror axis. The red (blue) arrow indicates the same meaning as in (a). (c) Néel ordered FM is present in, e.g. the $D_5$-symmetric Penrose QC, in which no symmetry operations relate the two sublattices. In (a-c), the red stars label the symmetry centers, and the solid (hollow) circles denote the sites in sublattice $\mathcal{A}$ ($\mathcal{B}$) and the solid lines represent the NN or NNN bonds.
• Figure 2: (a, b) The distribution of the magnetic moments in the $D_4$-symmetric Thue-Morse lattice hosting (a) 120 sites with the central 8-site cluster, and (b) 104 sites with the central 4-site cluster. In (a-b), the red (blue) dots represent spin-$\uparrow$ ($\downarrow$), and the size of each dot represents magnitude of the magnetic moment. The central black stars label the symmetry center and the solid lines with $t_1$ and $t_2$ represent the NN and NNN hoppings. (c, d) The spin-resolved spectral density difference $\mathcal{A}_\uparrow(\bm{p},\omega) - \mathcal{A}_\downarrow(\bm{p},\omega)$ as a function of momentum $\bm{p}$ for (c) the lattice exhibited in (a) with $\omega=-0.33t_1$, and (d) the lattice exhibited in (b) with $\omega=-0.2t_1$.
• Figure 3: (a) The distribution of the magnetic moment in the 104-site $D_2$-symmetric Thue-Morse lattice. (b) The spin-resolved spectral density difference $\mathcal{A}_{\uparrow}(\bm{p},\omega) - \mathcal{A}_{\downarrow}(\bm{p},\omega)$ as a function of momentum $\bm{p}$ for arbitrary $\omega$.
• Figure 4: The distribution of the magnetic moments in (a) the 86-site $D_5$-symmetric Penrose lattice, and (b) the 89-site $D_8$-symmetric Ammann-Beenker lattice. The average magnetic moment per site for each sublattice is shown in each figure.
• Figure A1: (a-e) The schematic diagram of $D_4$ symmetric Thue-Morse lattice with central 8-site cluster for (a), $D_4$ symmetric Thue-Morse lattice with central 4-site cluster for (b), $D_2$ symmetric Thue-Morse lattice for (c), $D_5$ symmetric Penrose lattice for (d) and $D_8$ symmetric Ammann-Beenker lattice for (e). The solid (hollow) circle denotes the site in sublattice $\mathcal{A}$ ($\mathcal{B}$) and the solid line represents the NN or NNN bond.