Majorana representation for dissipative spin systems

Abstract

The Majorana representation of spin operators allows for efficient field-theoretical description of spin-spin correlation functions. Any N-point spin correlation function is equivalent to a 2N-point correlator of Majorana fermions. For a certain class of N-point spin correlation functions (including "auto" and "pair-wise" correlations) a further simplification is possible, as they can be reduced to N-point Majorana correlators. As a specific example we study the Bose-Kondo model. We develop a path-integral technique and obtain the spin relaxation rate from a saddle point solution of the theory. Furthermore, we show that fluctuations around the saddle point do not affect the correlation functions as long as the latter involve only a single spin projection. For illustration we calculate the 4-point spin correlation function corresponding to the noise of susceptibility.

20 pages, 6 figures

References in corpus (5)

• Evidence for interacting two-level systems from the 1/f noise of a superconducting resonator
• Quantum phase transitions in the Bose-Fermi Kondo model
• Inelastic Microwave Photon Scattering off a Quantum Impurity in a Josephson-Junction Array
• Spin-spin correlators in Majorana representation
• Nonequilibrium Spin Noise and Noise of Susceptibility

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