Deconfined quantum criticality of nodal $d$-wave superconductivity, Néel order, and charge order on the square lattice at half-filling

Abstract

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 gauge-charged fermions are chosen so that they match with those of the spinons of the $\pi$-flux spin liquid. Global symmetries of all gauge-invariant observables are chosen to match with those of the particle-hole symmetric electronic Hubbard model at half-filling. Consequently, both the fundamental fermion and fundamental boson move in an average background $\pi$-flux, their gauge-invariant composite is the physical electron, and eliminating gauge fields in a strong gauge-coupling 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, valence-bond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases which 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 4 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 semi-metal phases.

47 pages, 20 figures

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• The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions
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• Vortex structure in a $d$-wave superconductor obtained by a confinement transition from the pseudogap metal
• Spin-Peierls instability of deconfined quantum critical points
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Thermopower across Fermi-volume-changing quantum phase transitions without translational symmetry breaking