Schwinger-Keldysh semionic approach for quantum spin systems

We derive a path-integral Schwinger-Keldysh approach for quantum spin syste ms. This is achieved by means of a semionic representation of spins as ferm ions with imaginary chemical potential. The major simplifying feature in co mparison with other representations (Holstein-Primakoff, Dyson-Maleev, slav e bosons/fermions, etc.) is that the local constraint is taken into account exactly. As a result, the standard diagram technique with the usual Feynma n coder is constructed. We illustrate the application of this technique for the Neel and spin-liquid states of the antiferromagnetic Heisenberg model.