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IIn the pseudogap regime of the cuprates, charge order breaks a$\mathbb{Z}_{2}$ symmetry. Therefore, the interaction of charge order andquenched disorder due to potential scattering, can, in principle, be treated asa random field Ising model. A numerical analysis of the ground state of such arandom field Ising model reveals local, glassy dynamics in both $2D$ and $3D$.The glassy dynamics are treated as a heat bath which couple to the itinerantelectrons, leading to an unusual electronic non-Fermi liquid. If the dynamicsare strong enough, the electron spectral function has no quasiparticle peak andthe effective mass diverges at the Fermi surface, precluding quantumoscillations. In contrast to charge density, $d$-density wave order (reflectingstaggered circulating currents) does not directly couple to potential disorder,allowing it to support quantum oscillations. At fourth order in Landau theory,there is a term consisting of the square of the $d$-density wave orderparameter, and the square of the charge order. This coupling could induceparasitic charge order, which may be weak enough for the Fermi liquid behaviorto remain uncorrupted. Here, we argue that this distinction must be made clear,as one interprets quantum oscillations in cuprates.

Random field disorder and charge order driven quantum oscillations in cuprates