Abstract
This paper consists of two important theoretical observations on the interplay betweenl = 2 condensates; d-density wave (ddw), electronic nematic and d-wave superconducting states. (1) Thereis SO(4) invariance at a transition between the nematic and d-wave superconducting states. Thenematic and d-wave pairing operators can be rotated into each other by pseudospinSU(2) generators, which are s-wave pairing and electron density operators.The difference between the current work and the previousO(4) symmetry at a transition between the ddw and d-wave superconducting states (Nayak 2000Phys. Rev. B 62 R6135) is presented. (2) The nematic and ddw operators transform intoeach other under a unitary transformation. Thus, when a Hamiltonian is invariant undersuch a transformation, the two states are exactly degenerate. The competition between thenematic and ddw states in the presence of a degeneracy breaking term is discussed.
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