Ring exchange, the exciton Bose liquid, and bosonization in two dimensions

Abstract

Motivated by the high-${T}_{c}$ cuprates, we consider a model of bosonic Cooper pairs moving on a square lattice via ring exchange. We show that this model offers a natural middle ground between a conventional antiferromagnetic Mott insulator and the fully deconfined fractionalized phase that underlies the spin-charge separation scenario for high-${T}_{c}$ superconductivity. We show that such ring models sustain a stable critical phase in two dimensions, the exciton Bose liquid (EBL). The EBL is a compressible state, with gapless but uncondensed boson and ``vortex'' excitations, power-law superconducting and charge-ordering correlations, and broad spectral functions. We characterize the EBL with the aid of an exact plaquette duality transformation, which motivates a universal low-energy description of the EBL. This description is in terms of a pair of dual bosonic phase fields, and is a direct analog of the well known one-dimensional bosonization approach. We verify the validity of the low-energy description by numerical simulations of the ring model in its exact dual form. The relevance to the high-${T}_{c}$ superconductors and a variety of extensions to other systems are discussed, including the bosonization of a two-dimensional fermionic ring model.