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Resorting to a recently developed theoretical device called dimensionalregularization for quantum criticality with a Fermi surface, we examine ametal-insulator quantum phase transition from a Landau's Fermi-liquid state toa U(1) spin-liquid phase with a spinon Fermi surface in two dimensions.Unfortunately, we fail to approach the spin-liquid Mott quantum critical pointfrom the U(1) spin-liquid state within the dimensional regularizationtechnique. Self-interactions between charge fluctuations called holons are notscreened, which shows a run-away renormalization group flow, interpreted asholons remain gapped. This leads us to consider another fixed point, where thespinon Fermi surface can be destabilized across the Mott transition. Based onthis conjecture, we reveal the nature of the spin-liquid Mott quantum criticalpoint: Dimensional reduction to one dimension occurs for spin dynamicsdescribed by spinons. As a result, Landau damping for both spin and chargedynamics disappear in the vicinity of the Mott quantum critical point. When theflavor number of holons is over its critical value, an interacting fixed pointappears to be identified with an inverted XY universality class, controlledwithin the dimensional regularization technique. On the other hand, afluctuation-driven first order metal-insulator transition results when it isbelow the critical number. We propose that the destabilization of a spinonFermi surface and the emergence of one-dimensional spin dynamics near thespin-liquid Mott quantum critical point can be checked out by spinsusceptibility with a $2 k_{F}$ transfer momentum, where $k_{F}$ is a Fermimomentum in the U(1) spin-liquid state: The absence of Landau damping in U(1)gauge fluctuations gives rise to a divergent behavior at zero temperature whileit vanishes in the presence of a spinon Fermi surface.

Spin-liquid Mott quantum criticality in two dimensions: Destabilization of a spinon Fermi surface and emergence of one-dimensional spin dynamics