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arXiv:cond-mat/9904142 · Physical review. B, Condensed matter

Projected SO(5) models

Shoucheng Zhang, Jiangping Hu, Enrico Arrigoni, Werner R. Hanke, Assa Auerbach

Published Nov 1, 1999• 52 citations
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Abstract

We construct a class of projected SO(5) models where the Gutzwiller constraint of no-double-occupancy is implemented exactly. We introduce the concept of projected SO(5) symmetry where all static correlation functions are exactly SO(5) symmetric and discuss the signature of the projected SO(5) symmetry in dynamical correlation functions. We show that this class of projected SO(5) models can give a realistic description of the global phase diagram of the high-${T}_{c}$ superconductors and account for many of their physical properties.

DOI
10.1103/physrevb.60.13070

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Zhang recently conjectured an approximate SO(5) symmetry relating antiferromagnetic and superconducting states in high- ${T}_{c}$ cuprates. Here, an exact SO(5) symmetry is implemented in a generalized Hubbard model (with long-range interactions) on a lattice. The possible relation to a more realistic extended Hubbard Hamiltonian is discussed.

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We construct a class of projected SO(5) models where the Gutzwiller constraint of no-double-occupancy is implemented exactly. We introduce the concept of projected SO(5) symmetry where all static correlation functions are exactly SO(5) symmetric and discuss the signature of the projected SO(5) symmetry in dynamical correlation functions. We show that this class of projected SO(5) models can give a realistic description of the global phase diagram of the high-Tc{T}_{c}Tc​ superconductors and account for many of their physical properties.
We present numerical studies of a quantum "projected" SO(5) model which aims at a unifying description of antiferromagnetism and superconductivity in the high- T(c) cuprates, while properly taking into account the Mott insulating gap. Our numerical results, obtained by the quantum Monte Carlo technique of stochastic series expansion, show that this model can give a realistic description of the global phase diagram of the high- T(c) superconductors and accounts for many of their physical properties. Moreover, we address the question of asymptotic restoring of the SO(5) symmetry at the critical point.
SU(4) dynamical symmetry is shown to imply a no-double-occupancy constraint on the minimal symmetry description of antiferromagnetism and ddd-wave superconductivity. This implies a maximum doping fraction of 14\frac{1}{4}41​ for cuprates and provides a microscopic critique of the projected SO(5) model. We propose that SU(4) superconductors are representative of a class of compounds that we term non-Abelian superconductors. We further suggest that non-Abelian superconductors may exist having SU(4) symmetry and therefore cupratelike dynamics, but without ddd-wave hybridization.
In this work, we present numerical results which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in the high-temperature superconductors. Using exact cluster diagonalization, we verify the recently proposed SO(5) multiplet structures for a widely used microscopic model, the t-J model. Our results show that the d-wave superconducting ground states away from half-filling are obtained from the higher spin states at half-filling through SO(5) rotations, that the dominant low energy resonance in the dynamical spin correlation function corresponds to a `pi-resonance' in the entire low doping region, and that the SO(5) symmetry is robust against inclusion of longer ranged Coulomb repulsion and next-nearest neighbor hopping.
We discuss properties of a recently proposed exactly SO(5)-symmetric ladder model. In the strong coupling limit we demonstrate how the SO(3)-symmetric description of spin ladders in terms of bond bosons can be upgraded to an SO(5)-symmetric bond-boson model, which provides a particularly simple example for the concept of SO(5) symmetry. Based on this representation we show that antiferromagnetism and superconductivity can be understood as condensation of either magnetic or charged bosons into a resonating-valence-bond vacuum. We identify exact eigenstates of a finite cluster with general multiplets of the SO(5) group, and present numerical results for the single particle, spin and charge spectra of the SO(5)-symmetric model and identify ``fingerprints'' of SO(5) symmetry in these. In particular we show that SO(5) symmetry implies a ``generalized rigid band behavior'' of the photoemission spectrum, i.e., spectra for the doped case are rigorously identical to spectra for spin-polarized states at half filling.
Zhang recently conjectured an approximate SO(5) symmetry relating antiferromagnetic and superconducting states in high- Tc{T}_{c}Tc​ cuprates. Here, an exact SO(5) symmetry is implemented in a generalized Hubbard model (with long-range interactions) on a lattice. The possible relation to a more realistic extended Hubbard Hamiltonian is discussed.