Antiferromagnetically Ordered State in the Half-Filled Hubbard Model on the Socolar Dodecagonal Tiling

Koga, Akihisa

doi:10.2320/matertrans.mt-mb2020003

Cited by 11 publications

(18 citation statements)

References 26 publications

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“…Similar states have been identified in the presence of gauge fields, called Aharonov-Bohm cages [19], and in some flatband models with nontrivial topology [20]. These states lie strictly at zero energy for bipartite lattices [21] and would be at the Fermi energy for the critically important case of half-filling [22][23][24]. For a periodic crystal, such strictly localized states can exist only if confined to a unit cell.…”

Section: Introductionsupporting

confidence: 55%

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Strictly localized states in the octagonal Ammann-Beenker quasicrystal

Oktel

2021

Phys. Rev. B

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Ammann-Beenker lattice is a two-dimensional quasicrystal with eightfold symmetry, which can be described as a projection of a cut from a four-dimensional simple cubic lattice. We consider the vertex tight-binding model on this lattice and investigate the strictly localized states at the center of the spectrum. We use a numerical method based on the generation of finite lattices around a given perpendicular space point and QR decomposition of the Hamiltonian to count the strictly localized states. We apply this method to count the frequency of localized states in lattices of up to 100 000 sites. We obtain an orthogonal set of compact localized states by diagonalizing the position operator projected onto the manifold spanned by the zero-energy states. We identify 20 localized state types and calculate their exact frequencies through their perpendicular space images. Unlike the Penrose lattice, all the localized state types are eightfold symmetric around an eight edge vertex, and all vertex types can support localized states. The total frequency of these 20 types gives a lower bound of f LS = 30 796 − 21 776 √ 2 0.085 47 for the fraction of strictly localized states in the spectrum. This value is in agreement with the numerical calculation and very close to the recently conjectured exact fraction of localized states f Ex = 3/2 − √ 2 0.085 79.

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Section: Introductionsupporting

confidence: 55%

“…The 14 types of LS in the third and fourth generation are displayed in real space below (Figs. [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The figures also show the allowed regions for their vertices in perpendicular space and the caption of each figure points out the reason for the independence of the LS type.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Strictly localized states in the octagonal Ammann-Beenker quasicrystal

Oktel

2021

Phys. Rev. B

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“…This transformation matrix for the number of spin-dependent tiles is diagonal with respect to the spin, implying that tiles with only one of the spins will appear in the thermodynamic limit. This property is distinct from that of the other twodimensional quasiperiodic tilings such as the Penrose [29], Ammann-Beenker [30], and Socolar dodecagonal tilings [31], where spin-dependent tiles appear equally in the thermodynamic limit. Immediately, we find a sublattice imbalance in ).…”

Section: Hexagonal Golden-mean Tilingmentioning

confidence: 76%

“…First, in Sec. II, we explain the hexagonal golden-mean tiling in detail, clarifying the existence of a sublattice imbalance which is distinct from that of the Penrose, Ammann-Beenker, and Socolar dodecagonal tilings [29][30][31]. In Sec.…”

Section: Introductionmentioning

confidence: 93%

“…To this end, magnetically ordered states on tilings have been well studied [26][27][28][29][30][31][32], with interesting magnetic properties reported under the Hubbard models on the Penrose [27,29], Ammann-Beenker [28,30], and Socolar dodecagonal tilings [31]. Here, no uniform magnetization appears in the thermodynamic limit, and antiferromagnetically ordered states are always realized when the Coulomb interaction is finite.…”

Section: Introductionmentioning

confidence: 99%

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Ferrimagnetically ordered states in the Hubbard model on the hexagonal golden-mean tiling

Koga,

Coates

2022

Preprint

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We study magnetic properties of the half-filled Hubbard model on the two-dimensional hexagonal goldenmean tiling. We find that the vertex model of the tiling is bipartite, with a sublattice imbalance of √ 5/(6τ 3 ) (where τ is the golden mean), and that the non-interacting tight-binding model gives macroscopically degenerate states at E = 0. We clarify that each sublattice has specific types of confined states, which in turn leads to an interesting spatial pattern in the local magnetizations in the weak coupling regime. Furthermore, this allows us to analytically obtain the lower bound on the fraction of the confined states as (τ + 9)/(6τ 6 ) ∼ 0.0986, which is conjectured to be the exact fraction. These results imply that a ferrimagnetically ordered state is realized even in the weak coupling limit. The introduction of the Coulomb interaction lifts the macroscopic degeneracy at the Fermi level, and induces finite staggered magnetization as well as uniform magnetization. Likewise, the spatial distribution of the magnetizations continuously changes with increasing interaction strength. The crossover behavior in the magnetically ordered states is also addressed in terms of the perpendicular space analysis.

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Superconducting Quasicrystals

Takemori

2024

Israel Journal of Chemistry

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Dan Shechtman's discovery of quasicrystals in 1982 introduced the scientific world to aperiodic crystals with unique rotational symmetries, redefining traditional crystallography. Although superconductivity in related periodic approximants has since been observed, true bulk superconductivity in quasicrystals was confirmed only in 2018. This recent discovery opens a new horizon not only for the study of correlated quasicrystals but more generally for the study of superconductivity with nontrivial spatial order. The theoretical understanding of superconducting quasicrystals poses challenges due to their lack of periodicity. Notably, they exhibit non‐BCS type superconductivity and distinct electromagnetic responses, reminiscent of the so‐called FFLO state. In this review, we provide an overview of superconducting quasicrystals, along with some “behind‐the‐scenes” information.

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Antiferromagnetically Ordered State in the Half-Filled Hubbard Model on the Socolar Dodecagonal Tiling

Cited by 11 publications

References 26 publications

Strictly localized states in the octagonal Ammann-Beenker quasicrystal

Strictly localized states in the octagonal Ammann-Beenker quasicrystal

Ferrimagnetically ordered states in the Hubbard model on the hexagonal golden-mean tiling

Superconducting Quasicrystals

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