SU(N) Self-Dual Sine-Gordon Model and Competing Orders

TL;DR

This paper explores a generalized SU(N) self-dual sine-Gordon model in one dimension, revealing its connection to conformal field theory and integrable models, and analyzing its role in quantum phase transitions and competing orders.

Contribution

It establishes the equivalence of the SU(N) self-dual sine-Gordon model to an SO(N)_2 conformal field theory with a current-current perturbation, providing new insights into quantum phase transitions.

Findings

Model describes quantum phase transitions from competing orders.

Equivalent to an SO(N)_2 conformal field theory with perturbation.

Discusses universality classes of the transitions.

Abstract

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.