SO(5) as a critical dynamical symmetry in the SU(4) model of high-temperature superconductivity

Abstract

An SU (4) model of high-temperature superconductivity and antiferromagnetism has recently been proposed. The SO(5) group employed by Zhang is embedded in this SU (4) as a subgroup, suggesting a connection between our SU (4) model and the Zhang SO(5) model. In order to understand the relationship between the the two models, we have used generalized coherent states to analyze the nature of the SO(5) subgroup. By constructing coherent-state energy surfaces, we demonstrate explicitly that the SU (4) ⊃ SO(5) symmetry can be interpreted as a critical dynamical symmetry interpolating between superconducting and antiferromagnetic phases, and that this critical dynamical symmetry has many similarities to critical dynamical symmetries identified previously in other fields of physics. More generally, we demonstrate with this example that the mathematical techniques associated with generalized coherent states may have powerful applications in condensed matter physics because they provide a clear connection between microscopic many-body theories and their broken-symmetry approximate solutions. In addition, these methods may be interpreted as defining the most general Bogoliubov transformation subject to a Lie group symmetry constraint, thus providing a mathematical connection between algebraic formulations and the language of quasiparticle theory. Finally, we suggest that the identification of the SO(5) symmetry as a critical dynamical symmetry implies deep algebraic connections between high-temperature superconductors and seemingly unrelated phenomena in other field of physics.

SU(4) Model of High-Temperature Superconductivity: Manifestation of Dynamical Symmetry in Cuprates

“…These pair operators, when supplemented with the multipole operators, close either an SO (8) or an Sp(6) algebra, depending on the choice of the basis 2 . If one neglects the fermionic degrees of freedom of these pairs and treats them as bosons, one has the early Interacting Boson Model 3 of Arima and Iachello.…”

“…As n/Ω decreases, the fluctuations become smaller and the energy surface tends more and more to the SU(2) SC limit. A symmetry limit having such a nature is termed a transitional or critical dynamical symmetry 8,23 . A critical dynamical symmetry is a dynamical symmetry having eigenstates that vary smoothly with a parameter (usually particle-number related) such that the eigenstates approximate one phase of the theory on one end of the parameter range and a different phase of the theory at the other end of the parameter range, with eigenstates in between exhibiting large softness against fluctuations in the order parameters describing the two phases.…”

Exact Solution of the Isovector Neutron-Proton Pairing Hamiltonian

“…SO(5) has also been proposed as the symmetry underlying high-T c superconductivity [12]. The exactly solvable RG model discussed in this Letter may conceivably be used to generalize SO(5) condensed-matter models [13] by the explicit addition of nondegenerate single-particle symmetry-breaking terms. Other possible applications might be found in polarized ultracold Fermi gases with p-wave pairing interactions [14].…”

Kondo effect in systems with dynamical symmetries

“…Now we turn to asymmetric configurations where E lc = E rc , Γ Tr = Γ T l . In this case the system loses the l − r symmetry, and it is more convenient to return to the initial variables used in the generic Hamiltonian (35).…”

“…In the presence of single-ion anisotropy the relation between the Hubbard operators for S = 1 and Gell-Mann matrices λ were established. It worth also mentioning in this context the SU (4) ⊃ SO(5) algebraic structure of superconducting and antiferromagnetic coherent states in cuprate High-T c materials 35 .…”