  We investigate the role of generic scale invariance in a Mott transition from
a U(1) spin-liquid insulator to a Landau Fermi-liquid metal, where there exist
massless degrees of freedom in addition to quantum critical fluctuations. Here,
the Mott quantum criticality is described by critical charge fluctuations, and
additional gapless excitations are U(1) gauge-field fluctuations coupled to a
spinon Fermi surface in the spin-liquid state, which turn out to play a central
role in the Mott transition. An interesting feature of this problem is that the
scaling dimension of effective leading local interactions between critical
charge fluctuations differs from that of the coupling constant between U(1)
gauge fields and matter-field fluctuations in the presence of a Fermi surface.
As a result, there appear dangerously irrelevant operators, which can cause
conceptual difficulty in the implementation of renormalization group (RG)
transformations. Indeed, we find that the curvature term along the angular
direction of the spinon Fermi surface is dangerously irrelevant at this
spin-liquid Mott quantum criticality, responsible for divergence of the
self-energy correction term in U(1) gauge-field fluctuations. Performing the RG
analysis in the one-loop level based on the dimensional regularization method,
we reveal that such extremely overdamped dynamics of U(1) gauge-field
fluctuations, which originates from the emergent one-dimensional dynamics of
spinons, does not cause any renormalization effects to the effective dynamics
of both critical charge fluctuations and spinon excitations. However, it turns
out that the coupling between U(1) gauge-field fluctuations and both
matter-field excitations still persists at this Mott transition, which results
in novel mean-field dynamics to explain the nature of the spin-liquid Mott
quantum criticality.
