Schwinger-Keldysh Semionic Approach for Quantum Spin Systems

Abstract

We derive a path-integral Schwinger-Keldysh approach for quantum spin systems. This is achieved by means of a semionic representation of spins as fermions with imaginary chemical potential. The major simplifying feature in comparison with other representations (Holstein-Primakoff, Dyson-Maleev, slave bosons/fermions, etc.) is that the local constraint is taken into account exactly. As a result, the standard diagram technique with the usual Feynman codex is constructed. We illustrate the application of this technique for the Néel and spin-liquid states of the antiferromagnetic Heisenberg model.

Resonance Kondo tunneling through a double quantum dot at finite bias

“…The scaling equations (13), (14) can also be derived in Schwinger-Keldysh formalism (see Refs. 28,33) by applying the "poor man's scaling" approach directly to the dot conductance 8 .…”

“…where f † ±1 are creation operators for fermions with spin "up" and "down" respectively, whereas f 0 stands for spinless fermion 32,33 . This representation can be generalized for SO(4) group by introducing another spinless fermion f s to take into consideration the singlet state.…”

Aging dynamics of quantum spin glasses of rotors

“…disordered and interacting electronic systems, 25,26 the infinite-range quantum p-spin glass in the spherical limit, 15 and a semionic representation for quantum spin systems. 27 In this paper, using the Schwinger-Keldysh dynamical approach, we investigate the aging behaviour of a spin glass of M component quantum rotors that have infinte range interactions and on site self interactions with a coefficient u. The model of quantum rotors is considerably simpler than that of true quantum Heisenberg spins present in any isotropic antiferromagnet or systems like the doped cuprates; the different components of the rotor variables all commute with each other, unlike the quantum spins.…”

Semi-Fermionic Representation for Spin Systems Under Equilibrium and Non-Equilibrium Conditions

“…Therefore, in this case the Kondo effect in DQD is induced by a strong external bias. The scaling equations can also be derived in Schwinger-Keldysh formalism (see 12 and also 19 ) by applying the "poor man's scaling" approach directly to the dot conductance. Thus, applying the semi-fermionic representation to the local (zerodimensional) problem with dynamical symmetry 48 we developed regular perturbation theory approach and obtained the scaling equations.…”

“…Finally, we show how to work with semi-fermions in real-time formalism and construct the Schwinger-Keldysh technique for SF. In this section, we will mostly follow original papers by the author 12 , 19 . The reader acquainted with semi-fermionic technique can easily skip this section.…”