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Semigroup Influence Matrices for Nonequilibrium Quantum Impurity Models.

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This summary is machine-generated.

We developed a new framework for quantum impurity models, using an effective semigroup influence matrix (SGIM) for accurate real-time dynamics. This method efficiently calculates spectral functions and relaxation rates, revealing Kondo physics in lossy systems.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Computational physics

Background:

  • Describing real-time quantum dynamics out of equilibrium is computationally challenging.
  • Existing methods for quantum impurity models face limitations in accuracy and evolution time.

Purpose of the Study:

  • Introduce a novel framework for real-time dynamics of quantum impurity models.
  • Overcome limitations of previous methods for accurate, long-time evolution.
  • Provide an efficient algorithm for obtaining the effective dynamical map.

Main Methods:

  • Developed an influence matrix approach using a semigroup influence matrix (SGIM).
  • Represented the SGIM using a uniform matrix-product state.
  • Presented an efficient algorithm for SGIM computation.
  • Benchmarked by computing spectral functions and relaxation rates.

Main Results:

  • Achieved high accuracy at long evolution times for quantum impurity models.
  • Successfully computed the spectral function of the single impurity Anderson model with high resolution.
  • Obtained relaxation rates of the impurity toward equilibrium after a quantum quench.
  • Confirmed the emergence of Kondo physics in a quantum impurity model with two-fermion loss.

Conclusions:

  • The SGIM framework offers a powerful and efficient method for studying non-equilibrium quantum impurity dynamics.
  • This approach enables accurate predictions of spectral properties and relaxation dynamics.
  • The framework successfully captures complex phenomena like Kondo physics in systems with dissipation.