Critical fluctuations in superconductors

Gauge Invariance at Large Charge

Quantum field theories with global symmetries simplify considerably in the large-charge limit allowing us to compute correlators via a semiclassical expansion in the inverse powers of the conserved charges. A generalization of the approach to gauge symmetries has faced the problem of defining gauge-independent observables and, therefore, has not been developed so far. We employ the large-charge expansion to calculate the scaling dimension of the lowest-lying operators carrying U(1) charge Q in the critical Abelian Higgs model in D=4-ε dimensions to leading and next-to-leading orders in the charge and all orders in the ε expansion. Remarkably, the results match our independent diagrammatic computation of the three-loop scaling dimension of the operator ϕ^{Q}(x) in the Landau gauge. We argue that this matching is a consequence of the equivalence between the gauge-independent dressed two-point function of Dirac type with the gauge-dependent two-point function of ϕ^{Q}(x) in the Landau gauge. We, therefore, shed new light on the problem of defining gauge-independent exponents which has been controversial in the literature on critical superconductors, as well as lay the foundation for large-charge methods in gauge theories.

New Easy-Plane CP^{N-1} Fixed Points

We study fixed points of the easy-plane CP^{N-1} field theory by combining quantum Monte Carlo simulations of lattice models of easy-plane SU(N) superfluids with field theoretic renormalization group calculations, by using ideas of deconfined criticality. From our simulations, we present evidence that at small N our lattice model has a first-order phase transition which progressively weakens as N increases, eventually becoming continuous for large values of N. Renormalization group calculations in 4-ε dimensions provide an explanation of these results as arising due to the existence of an N_{ep} that separates the fate of the flows with easy-plane anisotropy. When N<N_{ep}, the renormalization group flows to a discontinuity fixed point, and hence a first-order transition arises. On the other hand, for N>N_{ep}, the flows are to a new easy-plane CP^{N-1} fixed point that describes the quantum criticality in the lattice model at large N. Our lattice model at its critical point, thus, gives efficient numerical access to a new strongly coupled gauge-matter field theory.

Evidence for charged critical behavior in the pyrochlore superconductor RbOs2O6

We analyze magnetic penetration depth (lambda) data of the recently discovered superconducting pyrochlore oxide RbOs(2)O(6). Our results strongly suggest that in RbOs(2)O(6) charged critical fluctuations dominate the temperature dependence of lambda near T(c). This is in contrast with the mean-field behavior observed in conventional superconductors and the uncharged critical behavior found in nearly optimally doped cuprate superconductors. However, this finding agrees with the theoretical predictions for charged criticality and the charged criticality observed in underdoped YBa(2)Cu(3)O(6.59).