Abstract
Insulating quantum spin liquids can undergo a confinement transition to a valence bond solid via the condensation of topological excitations of the associated gauge theory. We extend the theory of such transitions to fractionalized Fermi liquids (FL*): These are metallic doped spin liquids in which the Fermi surfaces only have gauge neutral quasiparticles. Using insights from a duality transform on a doped quantum dimer model for the U(1)-FL* state, we show that projective symmetry group of the theory of the topological excitations remains unmodified, but the Fermi surfaces can lead to additional frustrating interactions. We propose a theory for the confinement transition of ${\mathbb{Z}}_{2}$-FL* states via the condensation of visons. A variety of confining, incommensurate density wave states are possible, including some that are similar to the incommensurate $d$-form factor density wave order observed in several recent experiments on the cuprate superconductors.
Highlights
The cuprate superconductors at low doping display a number of complex phenomena[1]
Our goal is to study this model with simple additional couplings allowed under the projective symmetry group (PSG) and investigating the resulting density-wave ground states with non-trivial form-factors
In the FL* phase, the gapless fermions do not carry a charge under the emergent gauge-field, and the PSG transformations for the topological excitations of the underlying gauge-theory remain unmodified
Summary
The cuprate superconductors at low doping display a number of complex phenomena[1]. Below the “pseudogap” temperature (T ∗), the metallic state displays Fermi-liquid like behavior[2,3] but is unlike any conventional metal in that the carrier density is inconsistent with the total Luttinger count[4]. For the case of conventional Landau-Ginzburg transitions, it is well-known that the theory for the onset of broken symmetry in insulators is very different from that in a metal: the presence of the Fermi surface over-damps the order parameter fluctuations, and this changes the nature of the critical fluctuations[37]. This feature does not extend to confining transitions in gauge theories because there is no ‘Yukawa’ coupling between the order parameter. The density of the fermionic dimers is x, while the total hole-concentration is (1 + x). (b) Pictorial illustration of the various terms in the dimer model defined by Eq (1)
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