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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Quantum information science

Background:

  • Global master equations, such as the Redfield master equation, require computationally intensive Hamiltonian diagonalization.
  • This diagonalization is a significant hurdle for studying interacting quantum many-body systems.
  • Existing local master equation approaches have limitations in their applicability.

Purpose of the Study:

  • To develop a method that bypasses the need for full Hamiltonian diagonalization in global master equations.
  • To establish a non-heuristic foundation for local master equations applicable to a broader range of systems.
  • To provide a more computationally tractable approach for quantum many-body system simulations.

Main Methods:

  • A short-bath-correlation-time expansion in reciprocal space is employed.
  • This leads to a series expansion of the jump operator, avoiding Hamiltonian diagonalization.
  • The local Redfield master equation is mapped to a novel local Lindblad form.

Main Results:

  • The method allows for an expansion of the global Redfield jump operator into local operators for locally coupled baths.
  • A new local Lindblad form is derived, extending the applicability of local master equations.
  • A non-heuristic foundation for local master equations is established.

Conclusions:

  • The developed expansion offers a computationally efficient alternative to full diagonalization for global master equations.
  • The novel local Lindblad form provides a powerful tool for simulating a wider array of quantum systems.
  • This work paves the way for combining advanced many-body techniques with robust local master equations.