Magnetic order and novel quantum criticality in the strongly interacting quasicrystals
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| Format: | Preprint |
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2025
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| _version_ | 1866908713119383552 |
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| author | Zhang, Cong Yu, Yin-Kai Shi, Shao-Hang Li, Zi-Xiang |
| author_facet | Zhang, Cong Yu, Yin-Kai Shi, Shao-Hang Li, Zi-Xiang |
| contents | 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 ($ν\approx 0.94$, $β\approx 0.72$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_13546 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Magnetic order and novel quantum criticality in the strongly interacting quasicrystals Zhang, Cong Yu, Yin-Kai Shi, Shao-Hang Li, Zi-Xiang Strongly Correlated Electrons Statistical Mechanics 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 ($ν\approx 0.94$, $β\approx 0.72$ 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. |
| title | Magnetic order and novel quantum criticality in the strongly interacting quasicrystals |
| topic | Strongly Correlated Electrons Statistical Mechanics |
| url | https://arxiv.org/abs/2512.13546 |