Magnetization without spin: effective Lagrangian of itinerant electrons

Abstract: Effective Lagrangian of itinerant electron system of finite density at finite magnetic field is found to include Chern-Simons term of electromagnetic potentials of lower scale dimension than those studied before. This term has an origin in many-body wave function and unique topological property that is independent of a spin degree of freedom. The coupling strength is proportional to $\frac{\rho}{eB}$, which is singular at $B=0$ for a constant charge density. The effective Lagrangian at a finite $B$ represents physical effects at $ B \neq 0$ properly. A universal shift of the magnetic field known as Slater-Pauling curve is derived from the effective Lagrangian.