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Interplay of Coulomb interaction and disorder in a two-dimensional semi-Dirac fermion system

It was recently found that Coulomb interaction can induce a series of nontrivial spectral and transport properties in a two-dimensional anisotropic Weyl semimetal. Different from graphehe that is basically an ordinary Fermi liquid, the Coulomb interaction in this system makes the Fermi liquid description invalid over a wide range of energy scales. We present a systematic renormalization group analysis of the interplay of Coulomb interaction and quenched disorder, and show that they have substantial mutual effects on each other, which then leads to a variety of quantum phase transitions and non-Fermi liquid behaviors. The low-energy physics of the system depends sensitively on the effective strength of Coulomb interaction and disorder.