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

Strongly Correlated Electrons