Fractional Quantum Hall States on CP2 Space
arXiv:2109.11522 · doi:10.1103/PhysRevResearch.5.023042
Abstract
We study four-dimensional fractional quantum Hall states on CP2 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 wavefunctions, the Determinant-Laughlin (Det-Laughlin) and Jastrow-Laughlin (Jas-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 quasi-hole degeneracy of Det-Laughlin state. The quasi-hole degeneracy exhibits an anomalous counting, indicating the existence of multiple forms of quasi-hole wavefunctions. We argue that these are captured by the mathematical framework of the "commutative algebra of N-points in the plane". We also generalize the pseudopotential formalism to dimensions higher than two, by considering coherent state wavefunction of bound states. The microscopic wavefunctions and Hamiltonians studied in this work pave the way for systematic study of high dimensional topological phase of matter that is potentially realizable in cold atom and optical experiments.
References in corpus (11)
- Non-Abelian Anyons and Topological Quantum Computation
- Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
- Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
- Topological quantum matter in synthetic dimensions
- Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
- Landau Level Quantization on the Sphere
- Topological Orders, Braiding Statistics, and Mixture of Two Types of Twisted Theories in Five Dimensions
- Ergodic Edge Modes in the 4D Quantum Hall Effect
- Entanglement entropy for integer quantum Hall effect in two and higher dimensions
- Geometric test for topological states of matter
- Theory of Four-dimensional Fractional Quantum Hall States