  The antiferromagnetic system on a rare-earth pyrochlore has been focused as a
strong candidate of U(1) quantum spin liquid. Here, we study the phase
transitions driven by external magnetic field and discuss the large thermal
Hall effect due to emergent spinon excitations with staggered gauge fields.
Despite the spinons, the charge excitations of the effective action that carry
spin-1/2 quantum number, do not couple to the external field, the emergent U(1)
gauge field is influenced in the presence of external magnetic field.
Especially along [111] and [110]-directions, we discuss the possible phase
transitions between U(1) spin liquids with different gauge fluxes are
stabilized in fields. Beyond the cases where gauge flux per plaquette are fixed
to be either 0 or $\pi$, there exists a regime where the staggered gauge fluxes
are stabilized without time reversal symmetry. In such a phase, the large
thermal Hall conductivity $\kappa_{xy}/T\sim 4.6\times
10^{-3}\text{W}/(\text{K}^2\cdot\text{m})$ is expected to be observed below 1K.
