Two-dimensional Quasicrystals Enable Exploration of Unique Magnetic Order and Critical Exponents

The behaviour of electrons in materials with highly ordered, yet non-repeating structures, known as quasicrystals, presents a fascinating challenge to conventional physics, and recent work by Cong Zhang, Yin-Kai Yu, and Shao-Hang Shi, along with Zi-Xiang Li and colleagues, sheds new light on this complex area.

The team investigated how the arrangement of atoms in these materials influences magnetic order and critical behaviour, revealing a surprising link between geometry and magnetism. Their simulations demonstrate that the specific aperiodic structure dictates whether magnetism appears immediately or requires a significant level of interaction between electrons, and importantly, they pinpoint a critical point in one quasicrystal exhibiting behaviour distinct from known magnetic materials. These findings establish a new understanding of how aperiodic order and electronic interactions combine to create novel forms of magnetic behaviour, potentially reshaping our understanding of critical phenomena in two dimensions.

Quasicrystals Host Novel Quantum Critical Points This research establishes a clear link between the geometry of aperiodic structures and the emergence of magnetic order, demonstrating that quasicrystals can host novel quantum critical points. By employing advanced Monte Carlo simulations, scientists investigated the half-filled Hubbard model on two distinct quasicrystalline lattices, Penrose and Thue-Morse, revealing fundamental differences in their magnetic behaviour. The Penrose tiling exhibits magnetic order even with extremely weak interactions, due to its unique electronic density of states, while the Thue-Morse lattice requires a stronger interaction to initiate the same transition. Crucially, the team identified a critical point on the Thue-Morse quasicrystal and determined that its critical exponents deviate significantly from those observed in conventional two-dimensional magnetic systems. This finding establishes the existence of a new universality class, driven by the interplay between electronic correlations and aperiodic geometry, challenging established paradigms of magnetic criticality.

Projector Monte Carlo Reveals Quasicrystal Criticality This research details a comprehensive investigation into quantum criticality within quasicrystalline materials, employing the Projector Quantum Monte Carlo method to model interacting electrons. Scientists focused on the Hubbard model, a simplified representation of electron behaviour, applied to both Penrose and Thue-Morse quasicrystalline lattices. The simulations aimed to understand how the aperiodic structure of these materials influences the emergence of magnetic order and the nature of quantum phase transitions.

The team carefully constructed trial wavefunctions, initial approximations of the system’s quantum state, to accelerate the simulations and ensure accuracy. They successfully mitigated the notorious ‘sign problem’ in quantum Monte Carlo calculations, a challenge that often hinders accurate results, by carefully choosing the trial wavefunction and exploiting the bipartite nature of the lattice. This allowed them to reliably determine the ground state properties and excitation spectra of the system. By analysing the system’s behaviour as it approached a critical point, the researchers extracted critical exponents, values that characterise the behaviour of physical quantities near a phase transition. They employed non-equilibrium relaxation dynamics, observing how the system evolved from a specific initial state, to determine these exponents. The resulting values deviate significantly from those observed in conventional two-dimensional magnetic systems, confirming the existence of a new universality class. Detailed analysis of the Binder ratio and squared order parameter, quantities that provide information about the system’s behaviour near the critical point, confirmed the accuracy of the obtained critical exponents. The data demonstrated a clear scaling relationship, validating the theoretical framework used to interpret the results. These findings provide strong evidence for a novel type of quantum criticality, driven by the unique interplay between electronic correlations and aperiodic geometry. 👉 More information 🗞 Magnetic order and novel quantum criticality in the strongly interacting quasicrystals 🧠 ArXiv: https://arxiv.org/abs/2512.13546 Tags: Rohail T. As a quantum scientist exploring the frontiers of physics and technology. My work focuses on uncovering how quantum mechanics, computing, and emerging technologies are transforming our understanding of reality. I share research-driven insights that make complex ideas in quantum science clear, engaging, and relevant to the modern world. Latest Posts by Rohail T.: Fluxonium Qubit Achieves Microwave Slow Light and Storage in Single-Atom System December 17, 2025 Quantum Biosensing Achieves 30-Minute Earlier Bacterial Growth Detection December 17, 2025 Quanvolutional Neural Networks Achieve Multi-Task Peak-Finding for Complex Molecular Spectra December 17, 2025