g=2 nonlinear sigma model revisited

We consider the transport properties of free fermions with gyromagnetic ratio g=2 in the presence of quenched disorder. This system has been shown to be closely related to the mean-field limit of various composite fermion theories [1,2,3]. We derive the nonlinear sigma model that describes the electrical and spin conductivities via the supersymmetric approach [4], and discuss its physical implications for various quantum phase transitions.

[1] Phys. Rev.B 98 (11) , 115105
[2] Phys. Rev.B 99 (23) , 235114
[3] ArXiv:1907.13141
[4] Adv. Phys. 32, 53 (1983)