Deconfined criticality between an antiferromagnetic insulator and a nodal d-wave superconductor: a quantum Monte Carlo study

We present a quantum Monte Carlo study of the transition between the insulating N\'eel state and the nodal $d$-wave superconductor on the square lattice at half-filling. We access a regime of frustrated magnetic order without a sign problem using a parton representation of the electron in terms of fermionic spinons and bosonic chargons. Both partons move in a background $\pi$-flux (so the electron experiences no net flux) and are coupled to a quantum fluctuating SU(2) lattice gauge field. In contrast to earlier studies directly on the electronic degrees of freedom, we find evidence for a second-order deconfined quantum phase transition at which both the N\'eel and $d$-wave superconductivity orders vanish continuously. We compute correlators of the spinon-chargon composite with the same quantum numbers as the electron: we find a gapless Dirac dispersion inside the $d$-wave superconductor, turning into a gapped dispersion in the antiferromagnet.