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Spin-spin correlators in the majorana representation.

Alexander Shnirman1, Yuriy Makhlin

  • 1Institut für Theoretische Festkörperphysik, Universität Karlsruhe, D-76128 Karlsruhe, Germany.

Physical Review Letters
|December 20, 2003
PubMed
Summary

This study introduces a new identity simplifying spin-spin correlator calculations in quantum systems. It connects these to simpler fermionic correlators, aiding analysis of spin dynamics and quantum measurements.

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Area of Science:

  • Quantum Mechanics
  • Condensed Matter Physics
  • Quantum Information Science

Background:

  • Calculating spin-spin correlators in quantum systems typically involves complex two-particle (four-fermion) correlators.
  • The Majorana representation offers an alternative framework for analyzing spin-1/2 systems.

Purpose of the Study:

  • To derive and present an identity relating spin-spin correlators to one-particle fermionic correlators.
  • To demonstrate the utility of this identity in analyzing complex quantum phenomena.

Main Methods:

  • Utilized the Majorana representation for a spin-1/2 system.
  • Derived a novel identity connecting spin-spin and one-particle fermionic correlators.

Main Results:

  • Established a direct relationship between spin-spin correlators and one-particle fermionic correlators.
  • This identity simplifies calculations compared to traditional four-fermion approaches.

Conclusions:

  • The derived identity offers a more efficient method for analyzing spin dynamics in dissipative environments.
  • This approach is applicable to understanding quantum detectors performing continuous qubit measurements.

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