Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Computational physics

Background:

• Calculating equilibrium properties of quantum systems coupled to baths is computationally challenging.
• Standard methods often struggle with strong system-bath coupling and large bath sizes.
• Approximating the reduced density matrix and effective Hamiltonian is crucial for understanding system behavior.

Purpose of the Study:

• To introduce a novel numerical algorithm for approximating the equilibrium-reduced density matrix and effective Hamiltonian.
• To generalize existing typicality algorithms for systems with strong spin-bath coupling.
• To provide a computationally efficient method for studying thermal equilibrium properties.

Main Methods:

• Generalization of typicality algorithms using trace estimators and Krylov subspace methods.
• Leveraging the concentration of reduced system density about its thermodynamic average.
• Numerical simulations and theoretical error analysis.

Main Results:

• The algorithm accurately approximates the equilibrium-reduced density matrix and effective Hamiltonian.
• Validation through theoretical error bounds and numerical experiments.
• Demonstration of the algorithm's potential for studying quantum phase transitions and entanglement entropy.

Conclusions:

• The developed numerical algorithm offers an accurate and efficient approach for quantum system analysis.
• The method is particularly useful for systems with strong system-bath interactions.
• This work opens new avenues for investigating complex quantum phenomena like phase transitions and entanglement.