Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2011-03-09
Phys. Rev. B 84, 085122 (2011)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
published version, more discussion added, some typos fixed
Scientific paper
10.1103/PhysRevB.84.085122
We study the thin torus limit of the Haldane-Rezayi state. Eight of the ten ground states are found to assume a simple product form in this limit, as is known to be the case for many other quantum Hall trial wave functions. The two remaining states have a somewhat unusual thin torus limit, where a "broken" pair of defects forming a singlet is completely delocalized. We derive these limits from the wave functions on the cylinder, and deduce the dominant matrix elements of the thin torus hollow-core Hamiltonians. We find that there are gapless excitations in the thin torus limit. This is in agreement with the expectation that local Hamiltonians stabilizing wave functions associated with non-unitary conformal field theories are gapless. We also use the thin torus analysis to obtain explicit counting formulas for the zero modes of the hollow-core Hamiltonian on the torus, as well as for the parent Hamiltonians of several other paired and related quantum Hall states.
Seidel Alexander
Yang Kun
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