Inclusion-Exclusion Principle for Open Quantum Systems with Bosonic Bath

Abstract

We present two fast algorithms which apply inclusion-exclusion principle to sum over the bosonic diagrams in bare diagrammatic quantum Monte Carlo (dQMC) and inchworm Monte Carlo method, respectively. In the case of inchworm Monte Carlo, the proposed fast algorithm gives an extension to the work ["Inclusion-exclusion principle for many-body diagrammatics", Phys. Rev. B, 98:115152, 2018] from fermionic to bosonic systems. We prove that the proposed fast algorithms reduce the computational complexity from double factorial to exponential. Numerical experiments are carried out to verify the theoretical results and to compare the efficiency of the methods.

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• Real-Time Simulation of Open Quantum Spin Chains with Inchworm Method
• Stark-Many body localization in interacting infinite dimensional systems
• Differential Equation Based Path Integral for System-Bath Dynamics
• Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation
• Simulation of Spin Chains with off-diagonal Coupling Using Inchworm Method
• Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm
• Transient Dynamical Phase Diagram of the Spin-Boson Model at Finite Temperature