Field Theory of Quantum Antiferromagnets : From the Triangular to the Kagome Lattice

We analyse a family of models, that interpolates between the Triangular lattice antiferromagnet (TLAF) and the Kagome lattice antiferromagnet (KLAF). We identify the field theories governing the low energy, long wavelength physics of these models. Near the TLAF the low energy field theory is a nonlinear sigma model of a SO(3) group valued field. The SO(3) symmetry of the spin system is enhanced to a $SO(3)_R \times SO(2)_L$ symmetry in the field theory. Near the KLAF other modes become important and the field takes values in $SO(3) \times S_2$. We analyse this field theory and show that it admits a novel phase in which the $SO(3)_R$ spin symmetry is unbroken and the $SO(2)_L$ symmetry is broken. We propose this as a possible mechanism by which a gapless excitation can exist in the KLAF without breaking the spin rotation symmetry.