Semi-fermionic representation of SU(N) Hamiltonians

Abstract:

We represent the generators of the SU(N) algebra as bilinear combinations of Fermi operators with imaginary chemical potential. The distribution function, consisting of a minimal set of discrete imaginary chemical potentials, is introduced to satisfy the local constraints. This representation leads to the conventional temperature diagram technique with standard Feynman codex, except that the Matsubara frequencies are determined by neither integer nor half-integer numbers. The real-time Schwinger-Keldysh formalism is formulated in the framework of complex equilibrium distribution functions for auxiliary semi-fermionic fields. We discuss the continuous large N and SU(2) large spin limits. We illustrate the application of this technique for magnetic and spin-liquid states of the Heisenberg model.