Sequencing the Entangled DNA of Fractional Quantum Hall Fluids

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 p...

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Bibliographic Details
Published in:Symmetry (Basel) 2023-02, Vol.15 (2), p.303
Main Authors: Cruise, Joseph R., Seidel, Alexander
Format: Article
Language:English
Subjects:
Dipoles
DNA
Electromagnetism
Fermions
Gene sequencing
Geometry
Hamiltonian functions
Mathematical analysis
Partons
Physics
Polynomials
Quantum field theory
Quantum Hall effect
Theorems
Wave functions
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Summary: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 V1 pseudo-potential, obtained via retention of only half the terms, stabilizes the ν=1/2 Tao–Thouless state as the unique densest ground state.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15020303