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• W3201414735 abstract "We study four-dimensional fractional quantum Hall states on ${mathbb{CP}}^{2}$ geometry from microscopic approaches. While in 2d the standard Laughlin wave function, given by a power of Vandermonde determinant, admits a product representation in terms of the Jastrow factor, this is no longer true in higher dimensions. In 4d, we can define two different types of Laughlin wave functions, the determinant-Laughlin and Jastrow-Laughlin states. We find that they are exactly annihilated by, respectively, two-particle and three-particle short-ranged interacting Hamiltonians. We then mainly focus on the ground state, low-energy excitations, and the quasihole degeneracy of determinant-Laughlin state. The quasihole degeneracy exhibits an anomalous counting, indicating the existence of multiple forms of quasihole wave functions. We argue that these are captured by the mathematical framework of ``commutative algebra of $Nmathrm{points}$ in the plane.'' The microscopic wave functions and Hamiltonians studied in this work pave the way for a systematic study of a high-dimensional topological phase of matter that is potentially realizable in cold atom and optical experiments." @default.
• W3201414735 created "2021-09-27" @default.
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• W3201414735 date "2023-04-20" @default.
• W3201414735 modified "2023-10-15" @default.
• W3201414735 title "Fractional quantum Hall states on <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi mathvariant=double-struck>C</mml:mi><mml:msup><mml:mi mathvariant=double-struck>P</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math> space" @default.
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• W3201414735 doi "https://doi.org/10.1103/physrevresearch.5.023042" @default.
• W3201414735 hasPublicationYear "2023" @default.
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