The SU(N) self-dual sine–Gordon model and competing orders

We investigate the low-energy properties of a generalized quantum sine–Gordon model in one dimension with a self-dual symmetry. This model describes a class of quantum phase transitions that stems from the competition of different orders. This SU(N) self-dual sine–Gordon model is shown to be equivalent to an SO(N)2 conformal field theory perturbed by a current–current interaction, which is related to an integrable fermionic model introduced by Andrei and Destri. In the context of spin-chain problems, we give several realizations of this self-dual sine–Gordon model and discuss the universality class of the transitions.