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- Title
Sequencing the Entangled DNA of Fractional Quantum Hall Fluids.
- Authors
Cruise, Joseph R.; Seidel, Alexander
- Abstract
We introduce and prove the "root theorem", which establishes a condition for families of operators to annihilate all root states associated with zero modes of a given positive semi-definite k-body Hamiltonian chosen from a large class. This class is motivated by fractional quantum Hall and related problems, and features generally long-ranged, one-dimensional, dipole-conserving terms. Our theorem streamlines analysis of zero-modes in contexts where "generalized" or "entangled" Pauli principles apply. One major application of the theorem is to parent Hamiltonians for mixed Landau-level wave functions, such as unprojected composite fermion or parton-like states that were recently discussed in the literature, where it is difficult to rigorously establish a complete set of zero modes with traditional polynomial techniques. As a simple application, we show that a modified V 1 pseudo-potential, obtained via retention of only half the terms, stabilizes the ν = 1 / 2 Tao–Thouless state as the unique densest ground state.
- Subjects
QUANTUM fluids; DNA sequencing; QUANTUM Hall effect; WAVE functions; QUANTUM theory
- Publication
Symmetry (20738994), 2023, Vol 15, Issue 2, p303
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym15020303