Comparison of the $pi$ and $Delta$ operator approximations for the two-dimensional t-J mode.pdf
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Comparison of the π and ? operator approximations
for the two-dimensional t-J model
Youngho Park
Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan
Abstract
We compare the spectra of the new π operator of the SO(5) theory and the con-
ventional ? operator for the two-dimensional t-J model. We also calculate the weight
transferred to the two-hole ground state from half-filling by these operators. We find
that the spectra of these operators are quite similar and the weight for the π operator
is smaller than the weight for the ? operator. We argue that the two-dimensional t-J
model does not have a good approximate SO(5) symmetry claimed in Ref. [1].
PACS: 71.27.+a,74.20.-z
1
The low-energy states of the two-dimensional t-J model have been often related to the
antiferromagnetism and the high-Tc superconductivity of the cuprate material [2]. The SO(5)
theory relates the spin excited state of the antiferromagnetic half-filling and the hole-doped
d-wave ground state of the high-Tc material by the π operator [3]. In other words, according
to the SO(5) theory in microscopic model Hamiltonians such as the two-dimensional t-
J and Hubbard models these two different states can be related by an SO(5) symmetry
group. Since the neutron scattering resonance in the cuprate YBCO was interpreted as the
π resonance, a low-energy resonance associated with the π operator [4], the basic idea of the
SO(5) theory has been highly controversial [5, 6]. Some numerical studies have been done
to support this theory by finding the π resonance for the dynamical correlation functions
of the π? (π) operator for the t-J and Hubbard models [1, 7, 8]. Eder et al. claimed that
low-energy states of the t-J model form SO(5) symmetry multiplets and the hole-doped
ground states away from half-filling are obtained from the higher-spin states at half-filling
through SO(5) rotations [1].
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