Abstract
We describe the localization transition of superfluids on two-dimensional lattices into commensurate Mott insulators with average particle density ( relatively prime integers) per lattice site. For bosons on the square lattice, we argue that the superfluid has at least degenerate species of vortices which transform under a projective representation of the square-lattice space group (a PSG). The formation of a single-vortex condensate produces the Mott insulator, which is required by the PSG to have density wave order at wavelengths of lattice sites ( integer) along the principle axes; such a second-order transition is forbidden in the Landau-Ginzburg-Wilson frame-work. We also discuss the superfluid-insulator transition in the direct boson representation and find that an interpretation of the quantum criticality in terms of deconfined fractionalized bosons is only permitted at special values of for which a permutative representation of the PSG exists. We argue [and demonstrate in detail in a companion paper: L. Balents et al., following paper, Phys. Rev. B 71, 144509 (2005)] that our results apply essentially unchanged to electronic systems with short-range pairing, with the PSG determined by the particle density of Cooper pairs. We also describe the effect of static impurities in the superfluid: the impurities locally break the degeneracy between the vortex species, and this induces density-wave order near each vortex. We suggest that such a theory offers an appealing rationale for the local density-of-states modulations observed by Hoffman et al. [Science 295, 466 (2002)], in scanning tunneling microscopy (STM) studies of the vortex lattice of and allows a unified description of the nucleation of density-wave order in zero and finite magnetic fields. We note signatures of our theory that may be tested by future STM experiments.
9 More- Received 6 September 2004
DOI:https://doi.org/10.1103/PhysRevB.71.144508
©2005 American Physical Society