Ginzburg-Landau approximation for the Hubbard model in the external magnetic field

TL;DR

This paper applies Ginzburg-Landau theory to analyze the Hubbard model under an external magnetic field, focusing on the metal-insulator transition near half-filling, and derives analytical solutions for homogeneous cases.

Contribution

It introduces a phenomenological Ginzburg-Landau approach to the Hubbard model in magnetic fields, providing analytical insights into the metal-insulator transition.

Findings

Critical magnetic field for metal-insulator transition identified

Analytical solutions for homogeneous distributions derived

Interaction effects between opposite spins incorporated

Abstract

The Hubbard model is studied in the external magnetic field. The analysis is carried out phenomenologically within the framework of the Ginzburg-Landau theory with the order parameter describing the opposite spin electrons. The study is performed for the nearly half-filled lower Hubbard band in the metallic state. The final equations are the Pauli-like ones for the opposite spins and nonlinear as a result of interaction between electrons with the opposite spins. The equations can analytically be solved for the spatially homogeneous distributions in a number of most interesting cases. In particular, the problem on the metal-insulator transition is analyzed for the nearly half-filled Hubbard sub-bands. The critical magnetic field at which the transition from the metallic state to the insulator one takes place is found under the paramagnetic spin effect.