Inclusion–exclusion principle for open quantum systems with bosonic bath

Siyao Yang,Jianfeng Lu,Zhenning Cai

doi:10.1088/1367-2630/ac02e1

Siyao Yang, Jianfeng Lu + Show 1 more

Open Access

https://doi.org/10.1088/1367-2630/ac02e1

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Abstract

We present two fast algorithms which apply inclusion–exclusion principle to sum over the bosonic diagrams in bare diagrammatic quantum Monte Carlo and inchworm Monte Carlo method, respectively. In the case of inchworm Monte Carlo, the proposed fast algorithm gives an extension to the work [2018 Inclusion–exclusion principle for many-body diagrammatics Phys. Rev. B 98 115152] 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.

Highlights

Open quantum systems, which characterize quantum systems coupled with environment, have been studied extensively for many decades, as it arises in many context including quantum optics [9], quantum computation [31], and dynamical mean field theory [20], just to list a few
Developed based on ansatz of wave functions. While these deterministic methods require some additional modeling of the open quantum system, the bare diagrammatic quantum Monte Carlo method [22] applies Monte Carlo sampling to directly compute the summations and high-dimensional integrals in the Dyson series expansion of the quantum observable [37], and after applying Wick’s theorem [30], this approach can be represented as the summation of all possible diagrams, each of which is determined by a finite time sequences and a partition of them into pairs
We have proposed fast algorithms based on inclusion-exclusion principle to sum diagrams appearing in the bare diagrammatic quantum Monte Carlo (dQMC) and inchworm Monte Carlo method

Summary

Introduction

Open quantum systems, which characterize quantum systems coupled with environment, have been studied extensively for many decades, as it arises in many context including quantum optics [9], quantum computation [31], and dynamical mean field theory [20], just to list a few. The quasi-adiabatic propagator path integral (QuAPI) [25, 26] method assumes finite memory length and so that the path integral can be numerically computed iteratively; by assuming that the bath response function has a special form, the hierarchical equations of motion can be applied [38, 39]; the method of multiconfiguration time dependent Hartree (MCTDH) [3] is developed based on ansatz of wave functions While these deterministic methods require some additional modeling of the open quantum system, the bare diagrammatic quantum Monte Carlo (dQMC) method [22] applies Monte Carlo sampling to directly compute the summations and high-dimensional integrals in the Dyson series expansion of the quantum observable [37], and after applying Wick’s theorem [30], this approach can be represented as the summation of all possible diagrams, each of which is determined by a finite time sequences and a partition of them into pairs.

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