We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gaugecharged fermions are chosen so that they match with those of the spinons of the$\pi $flux spin liquid. Global symmetries of all gaugeinvariant observables are chosen to match with those of the particlehole symmetric electronic Hubbard model at halffilling. Consequently, both the fundamental fermion and fundamental boson move in an average background$\pi $flux, their gaugeinvariant composite is the physical electron, and eliminating gauge fields in a strong gaugecoupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodal$d$wave superconductor, and states with Néel, valencebond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases that are very likely described by$(2+1)$dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventional$d$wave superconductor with gapless Bogoliubov quasiparticles at four nodal points in the Brillouin zone. We also apply our approach to the honeycomb lattice, where we find a bicritical point at the junction of Néel, valence bond solid (Kekulé), and Dirac semimetal phases.
We analyze a Higgs transition from a U(1) Dirac spin liquid to a gapless ℤ_{2}spin liquid. This ℤ_{2}spin liquid is of relevance to the spin
 Award ID(s):
 2002850
 NSFPAR ID:
 10482001
 Publisher / Repository:
 Journal of High Energy Physics
 Date Published:
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2022
 Issue:
 7
 ISSN:
 10298479
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Published by the American Physical Society 2024 
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