Numerical evaluation and robustness of the quantum mean force Gibbs state

Abstract

We introduce a numerical method to determine the Hamiltonian of Mean Force (HMF) Gibbs state for a quantum system strongly coupled to a reservoir. The method adapts the Time Evolving Matrix Product Operator (TEMPO) algorithm to imaginary time propagation. By comparing the real-time and imaginary-time propagation for a generalized spin-boson model, we confirm that the HMF Gibbs state correctly predicts the steady state. We show that the numerical dynamics match the polaron master equation at strong coupling. We illustrate the potential of the imaginary-time TEMPO approach by exploring reservoir-induced entanglement between qubits.

8 pages, 7 figures

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• OQuPy: A Python package to efficiently simulate non-Markovian open quantum systems with process tensors
• Effective-Hamiltonian theory: An approximation to the equilibrium state of open quantum systems
• Bath-engineering magnetic order in quantum spin chains: An analytic mapping approach
• The wave operator representation of quantum and classical dynamics
• Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems
• Stochastic simulation of dissipative quantum oscillators
• Structure of the Hamiltonian of mean force
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• Path Integral Formalism for Quantum Open Systems
• Structure of Quantum Mean Force Gibbs States for Coupled Harmonic Systems
• Faster randomized partial trace estimation