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Comparison of the $pi$ and $Delta$ operator approximations for the two-dimensional t-J mode.pdf

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a r X i v : c o n d - m a t / 9 9 0 7 4 3 7 v 1 [ c o n d - m a t .s t r - e l ] 2 8 J u l 1 9 9 9 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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