  We show using quantum free energy calculation that the quantum phase
transition between U(1) quantum spin liquid (QSL) and antiferromagnet (AFM)
phases in pyrochlore quantum antiferromagnet (QAFM) is a first order rather
than second order. This change in order from second to first order is induced
by gauge fluctuations, which are explicitly taken into account at gauge theory
level in our effective low energy theory. We therefore have discovered a
fluctuation-induced first order quantum phase transition in pyrochlore QAFM. We
explicitly derive the quantum free energy description of this QSL to AFM phase
transition and show that it is a weakly first order phase transition. We also
briefly discuss the experimental relevance of this result.
