Chern-Simons theory for frustrated quantum magnets

We study the problem of frustrated quantum magnets by mapping models with Heisenberg spins, which are hard-core bosons, onto a problem of fermions coupled to a Chern-Simons gauge field [1]. Similar methods have been used successfully in the case of unfrustrated systems like the square lattice [2]. However, in the case of frustrated systems there always exists some arbitrariness in defining the problem. At the mean-field level these issues can be over looked but the effects of fluctuations, which are generally strong in these systems, are expected to alter the mean-field physics [3-4]. We discuss the difficulties involved in setting up this problem on a triangular or kagome lattice and some approaches to tackle these issues. We study the effects of fluctuations in these systems and the possibility of spin-liquid type phases.\\[4pt] [1] E. Fradkin, Phys. Rev. Lett. 63, 322-325 (1989)\\[0pt] [2] A. Lopez, A. G. Rojo, and E. Fradkin, Phys. Rev. B 49, 15139 (1994)\\[0pt] [3] G. Misguich, Th. Jolicoeur, and S. M. Girvin Phys. Rev. Lett. 87, 097203 (2001)\\[0pt] [4] Kun Yang, L. K. Warman and S. M. Girvin, Phys. Rev. Lett. 70, 2641 (1993)