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

TL;DR

This study uses CDMFT to explore the magnetic phase diagram and spectral properties of the anisotropic square lattice Hubbard model, revealing different transition mechanisms and quantum critical behavior driven by lattice anisotropy.

Contribution

It provides a detailed phase diagram of the anisotropic Hubbard model at half-filling, highlighting the role of anisotropy in magnetic transitions and quantum criticality.

Findings

Paramagnetic metal stabilized by next-nearest-neighbor hopping.

First-order Mott transition associated with local moment ordering.

Quantum critical behavior in strongly anisotropic regime.

Abstract

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