Ginzburg-Landau Theory and Classical Critical Phenomena of Mott Transition

Theory of classical critical phenomena of Mott transition is developed for the dimensionality $d \le \infty$. Reconsidering a cluster dynamical mean-field theory (DMFT), Ginzburg-Landau free energy is derived in terms of hybridization function for a cluster-impurity model. Its expansion around a cluster DMFT solution reduces to a $\phi^4$ model. Inherent thermal Mott transition without spontaneous symmetry breaking is described by a scalar field reflecting the charge degrees of freedom. In the space of local Coulomb repulsion, chemical potential and temperature, a first-order transition surface terminates at a critical end curve. The criticality belongs to the Ising universality as a liquid-gas transition. Various quantities including double occupancy, electron filling and entropy show diverging responses at the criticality and discontinuities at the first-order transition. Particularly, electron effective mass shows a critical divergence in $2\le d\le 4$. Only at a certain curve on the surface, a filling-control transition and its related singularities disappear. We discuss detailed critical behaviors, effects of interplay with other critical fluctuations, and relevant experimental results.