Jain-2/5 parent Hamiltonian: Structure of zero modes, dominance patterns, and zero mode generators

Article

关键词: QUANTUM HALL STATES;    NON-ABELIAN STATISTICS;    EDGE EXCITATIONS;    HIERARCHY;    SYSTEMS;    FLUID;   

DOI  :  10.1103/PhysRevB.95.195169

来源: SCIE

【 摘 要 】

We analyze general zero mode properties of the parent Hamiltonian of the unprojected Jain-2/5 state. We characterize the zero mode condition associated to this Hamiltonian via projection onto a four-dimensional two-particle subspace for given pair angular momentum, for the disk and similarly for the spherical geometry. Earlier numerical claims in the literature about ground-state uniqueness on the sphere are substantiated on analytic grounds, and related results are derived. Preference is given to second-quantized methods, where zero mode properties are derived not from given analytic wave functions, but from a lattice Hamiltonian and associated zero mode conditions. This method reveals new insights into the guiding-center structure of the unprojected Jain-2/5 state, in particular, a system of dominance patterns following a generalized Pauli principle, which establishes a complete one-to-one correspondence with the edge mode counting. We also identify one-body operators that function as generators of zero modes.

【 授权许可】

Free