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Search for exact local Hamiltonians for general fractional quantum Hall states

Title
Search for exact local Hamiltonians for general fractional quantum Hall states
Authors
Sreejith G.J.Fremling M.Jeon G.S.Jain J.K.
Ewha Authors
전건상
SCOPUS Author ID
전건상scopus
Issue Date
2018
Journal Title
Physical Review B
ISSN
2469-9950JCR Link
Citation
Physical Review B vol. 98, no. 23
Publisher
American Physical Society
Indexed
SCI; SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
We report on our systematic attempts at finding local interactions for which the lowest-Landau-level projected composite-fermion wave functions are the unique zero energy ground states. For this purpose, we study in detail the simplest nontrivial system beyond the Laughlin states, namely, bosons at filling factor ν=2/3, and identify local constraints among clusters of particles in the ground state. By explicit calculation, we show that no Hamiltonian up to (and including) four-particle interactions produces this state as the exact ground state and speculate that this remains true even when interaction terms involving a greater number of particles are included. Surprisingly, we can identify an interaction, which imposes an energetic penalty for a specific entangled configuration of four particles with relative angular momentum of 6 that produces a unique zero energy solution (as we have confirmed for up to 12 particles). This state, referred to as the λ state, is not identical to the projected composite-fermion state, but the following facts suggest that the two might be topologically equivalent: the two states have a high overlap, they have the same root partition, the quantum numbers for their neutral excitations are identical, and the quantum numbers for the quasiparticle excitations also match. On the quasihole side, we find that even though the quantum numbers of the lowest energy states agree with the prediction from the composite-fermion theory, these states are not separated from the others by a clearly identifiable gap. This prevents us from making a conclusive claim regarding the topological equivalence of the λ state and the composite-fermion state. Our study illustrates how new candidate states can be identified from constraining selected many-particle configurations and it would be interesting to pursue their topological classification. © 2018 American Physical Society.
DOI
10.1103/PhysRevB.98.235139
Appears in Collections:
자연과학대학 > 물리학전공 > Journal papers
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