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We study the uniform time reversal invariant $U(1)$ quantum spin liquid (QSL)with low energy fermionic quasi-particles for rare earth pyrochlore magnets andexplore its magnetic instability employing an augmented fermionic parton meanfield theory approach. Self consistent calculations stabilise an uniform $U(1)$QSL with both gapped and gapless parton excitations as well as fractionalisedmagnetically ordered phases in an experimentally relevant part of the phasediagram near the classical phase boundaries of the magnetically ordered phases.The gapped QSL has a band-structure with a non-zero $Z_2$ topologicalinvariant. The fractionalised magnetic ordered phases bears signature of bothQSL through fermionic excitations as well as magnetic order. Thus this providesa possible way to understand the unconventional diffuse neutron scattering inrare-earth pyrochlores such as Yb$_2$Ti$_2$O$_7$, Er$_2$Sn$_2$O$_7$ andEr$_2$Pt$_2$O$_7$ at low/zero external magnetic fields. We calculate thedynamic spin structure factor to understand the nature of the diffusetwo-particle continuum.

Interplay of uniform U(1) quantum spin liquid and magnetic phases in rare earth pyrochlore magnets : a fermionic parton approach