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.
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.
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.
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 that low-energy states of the $t\ensuremath{-}J$ model, a widely used microscopic model for the high-Tc cuprates, form SO(5) symmetry multiplets. 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. The SO(5) symmetry is found to be robust against the inclusion of longer-ranged Coulomb repulsion and next-nearest-neighbor hopping.
We revisit the problem of interacting electrons hopping on a two-leg ladder. A perturbative renormalization-group analysis reveals that at half-filling the model scales onto an exactly soluble Gross-Neveu model for arbitrary finite-ranged interactions, provided they are sufficiently weak. The Gross-Neveu model has an enormous global SO(8) symmetry, manifest in terms of eight real Fermion fields that, however, are highly nonlocal in terms of the electron operators. For generic repulsive interactions, the two-leg ladder exhibits a Mott insulating phase at half-filling with d-wave pairing correlations. Integrability of the Gross-Neveu model is employed to extract the exact energies, degeneracies, and quantum numbers of all the low-energy excited states, which fall into degenerate SO(8) multiplets. One SO(8) vector includes two charged Cooper pair excitations, a neutral s=1 triplet of magnons, and three other neutral s=0 particle-hole excitations. A triality symmetry relates these eight two-particle excitations to two other degenerate octets, which are comprised of single-electron-like excitations. In addition to these 24 degenerate ``particle'' states costing an energy (mass) m to create, there is a 28-dimensional antisymmetric tensor multiplet of ``bound'' states with energy 3m. Doping away from half-filling liberates the Cooper pairs, leading to quasi-long-range d-wave pair field correlations, but maintaining a gap to spin and single-electron excitations. For very low doping levels, integrability allows one to extract exact values for these energy gaps. Enlarging the space of interactions to include attractive interactions reveals that there are four robust phases possible for the weak coupling two-leg ladder. While each of the four phases has a (different) SO(8) symmetry, they are shown to all share a common SO(5) symmetry---the one recently proposed by Zhang as a unifying feature of magnetism and superconductivity in the cuprates.
We construct a family of electronic-ladder models with SO(5) symmetry that have exact ground states in the form of finitely correlated wave functions. Extensions for these models preserving this symmetry are studied using these states in a variational approach. Within this approach, the zero-temperature phase diagram of these electronic ladders at half filling is obtained, reproducing the known results in the weak coupling (band insulator) and strong-coupling regime, first studied by Scalapino, Zhang, and Hanke. Finally, the compact form of the variational wave functions allows us to compute various correlation functions for these systems.
We construct an SO(5) symmetric electron model on a two-chain ladder with purely local interactions on a rung. The ground state phase diagram of this model is determined in the strong-coupling limit. The relationship between the spin-gap magnon mode of the spin-gap insulator and the $\ensuremath{\pi}$ resonance mode of the d-wave pairing phase is discussed. We also present the exact ground state for an SO(5) superspin model.