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Using a cluster extension of the dynamical mean-field theory (CDMFT) we mapout the magnetic phase diagram of the anisotropic square lattice Hubbard modelwith nearest-neighbor intrachain $t$ and interchain $t_{\perp}$ hoppingamplitudes at half-filling. A fixed value of the next-nearest-neighbor hopping$t'=-t_{\perp}/2$ removes the nesting property of the Fermi surface andstabilizes a paramagnetic metal phase in the weak-coupling regime. In theisotropic and moderately anisotropic regions, a growing spin entropy in themetal phase is quenched out at a critical interaction strength by the onset oflong-range antiferromagnetic (AF) order of preformed local moments. It givesrise to a first-order metal-insulator transition consistent with theMott-Heisenberg picture. In contrast, a strongly anisotropic regime$t_{\perp}/t\lesssim 0.3$ displays a quantum critical behavior related to thecontinuous transition between an AF metal phase and the AF insulator. Hence,within the present framework of CDMFT, the opening of the charge gap ismagnetically driven as advocated in the Slater picture. We also discuss how thelattice-anisotropy-induced evolution of the electronic structure on a metallicside of the phase diagram is tied to the emergence of quantum criticality.

Local moments versus itinerant antiferromagnetism: magnetic phase diagram and spectral properties of the anisotropic square lattice Hubbard model