Monopole Quantum Numbers in the Staggered Flux Spin Liquid

Abstract

Algebraic spin liquids, which are exotic gapless spin states preserving all microscopic symmetries, have been widely studied due to potential realizations in frustrated quantum magnets and the cuprates. At low energies, such putative phases are described by quantum electrodynamics in 2+1 dimensions. While significant progress has been made in understanding this nontrivial interacting field theory and the associated spin physics, one important issue which has proved elusive is the quantum numbers carried by so-called monopole operators. Here we address this issue in the ``staggered-flux'' spin liquid which may be relevant to the pseudogap regime in high-T_c. Employing general analytical arguments supported by simple numerics, we argue that proximate phases encoded in the monopole operators include the familiar Neel and valence bond solid orders, as well as other symmetry-breaking orders closely related to those previously explored in the monopole-free sector of the theory. Surprisingly, we also find that one monopole operator carries trivial quantum numbers, and briefly discuss its possible implications.

9 pages, 0 figures; minor clarifications

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• Deconfined quantum criticality of nodal $d$-wave superconductivity, Néel order, and charge order on the square lattice at half-filling
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• Continuous transition between Ising magnetic order and a chiral spin liquid
• Symmetry-breaking effects of instantons in parton gauge theories
• Dirac spin liquid as an "unnecessary" quantum critical point on square lattice antiferromagnets
• Vortex structure in a $d$-wave superconductor obtained by a confinement transition from the pseudogap metal
• Fractionalized Fermi liquids and the cuprate phase diagram
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