Semigroup Influence Matrices for Nonequilibrium Quantum Impurity Models

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.