Quantum impurity models coupled to Markovian and non-Markovian baths

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Quantum information

Background:

• Quantum impurity models describe small interacting quantum systems coupled to an environment.
• Studying the reduced density matrix evolution is crucial for understanding system dynamics.
• Existing methods may not fully capture effects of additional Markovian baths.

Purpose of the Study:

• To develop a novel method for studying quantum impurity models with generic nonlinear coupling to an environment.
• To compute the evolution operator of the reduced density matrix of the impurity.
• To incorporate the effects of an additional Markovian quantum bath.

Main Methods:

• Derivation of an exact real-time hybridization expansion for the evolution operator.
• Generalization of existing results to include Markovian dissipation.
• Formulation of a Dyson equation for the reduced density matrix evolution.
• Evaluation of the self-energy using the noncrossing approximation.

Main Results:

• An exact real-time hybridization expansion applicable to quantum impurity models with Markovian dissipation was derived.
• The method generalizes previous results and is potentially amenable to stochastic sampling via diagrammatic Monte Carlo.
• A Dyson equation was established, and its self-energy was evaluated using the noncrossing approximation.
• The approach was successfully applied to a fermionic impurity model with specific environmental interactions.

Conclusions:

• The developed method provides a powerful tool for analyzing quantum impurity models under complex environmental conditions.
• The hybridization expansion and Dyson equation offer new avenues for theoretical and computational studies.
• The application to a fermionic impurity model demonstrates the practical utility of the approach.