Thermal SU(2) lattice gauge theory for intertwined orders and hole pockets in the cuprates

The cuprate pseudogap phase displays Fermi arc spectral weight in photoemission and scanning tunneling microscopy (STM), while recent magnetotransport observations yield evidence for the existence of hole pockets of fractional area $p/8$, where $p$ is the doping density. We present a Monte Carlo study of a thermal SU(2) lattice gauge theory which can reconcile these observations. Our simulation includes the SU(2) gauge field $U$ of a $\pi$-flux spin liquid, and a SU(2) fundamental charge $e$ Higgs boson $B$. There is a Yukawa coupling between $B$, the fermionic spinons of the spin liquid, and the hole pockets of a fractionalized Fermi liquid. At the higher temperatures of the pseudogap, the finite-doping sign problem is evaded by including only thermal fluctuations of $B$ and $U$, while the fermions are diagonalized exactly for each boson background. Our study also yields a fractionalized description of intertwined orders at lower temperatures, including the onset of $d$-wave superconductivity by the expulsion of vortices with flux $h/(2e)$, each with charge-order halos. We discuss conditions under which quantum oscillations in the density of states from hole pockets of area $p/8$ could be observable in clean under-hole-doped cuprates.