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Journal of the Physical Society of Japan

Equivalence of Two Types of Singlet Wave Functions for the Triangular Lattice Antiferromagnet

Yukio Okwamoto, Shu-ichi Nagasawa

Published Aug 15, 1990• 1 citation
Publisher

Abstract

A one-body problem on the triangular lattice is solved in the presence of a fictitious magnetic field which produces a quarter of a flux quantum through each triangle. Then it is shown explicitly that the fractional quantum Hall wave function for a ground state of the s =1/2 triangular lattice antiferromagnet is equivalent to a variational singlet wave function written by a pair of determinants which are made out of eigenfunctions of the one-body problem.

DOI
10.1143/jpsj.59.2621

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A one-body problem on the triangular lattice is solved in the presence of a fictitious magnetic field which produces a quarter of a flux quantum through each triangle. Then it is shown explicitly that the fractional quantum Hall wave function for a ground state of the s =1/2 triangular lattice antiferromagnet is equivalent to a variational singlet wave function written by a pair of determinants which are made out of eigenfunctions of the one-body problem.
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We characterize in detail a wave function conceivable in fractional quantum Hall systems where a spin or equivalent degree of freedom is present. This wave function combines the properties of two previously proposed quantum Hall wave functions, namely the non-Abelian spin-singlet state and the nonunitary Gaffnian wave function. This is a spin-singlet generalization of the spin-polarized Gaffnian, which we call the ``spin-singlet Gaffnian'' (SSG). In this paper we present evidence demonstrating that the SSG corresponds to the ground state of a certain local Hamiltonian, which we explicitly construct, and, further, we provide a relatively simple analytic expression for the unique ground-state wave functions, which we define as the zero energy eigenstates of that local Hamiltonian. In addition, we have determined a certain nonunitary, rational conformal field theory which provides an underlying description of the SSG and we thus conclude that the SSG is ungapped in the thermodynamic limit. In order to verify our construction, we implement two recently proposed techniques for the analysis of fractional quantum Hall trial states: The ``spin dressed squeezing algorithm,'' and the ``generalized Pauli principle.''