Accelerated impurity solver for DMFT and its diagrammatic extensions

• Published in: Computer physics communications 2021-10, Vol.267 (C), p.108075, Article 108075
• Main Authors: Melnick, Corey, Sémon, Patrick, Yu, Kwangmin, D'Imperio, Nicholas, Tremblay, André-Marie, Kotliar, Gabriel
• Format: Article
• Language: English
• Subjects: Anderson impurity model; Dynamical mean field theory; Quantum impurity solver; Quantum Monte Carlo; Strongly-correlated materials
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2021.108075

We present ComCTQMC, a GPU accelerated quantum impurity solver. It uses the continuous-time quantum Monte Carlo (CTQMC) algorithm wherein the partition function is expanded in terms of the hybridisation function (CT-HYB). ComCTQMC supports both partition and worm-space measurements, and it uses improved estimators and the reduced density matrix to improve observable measurements whenever possible. ComCTQMC efficiently measures all one and two-particle Green's functions, all static observables which commute with the local Hamiltonian, and the occupation of each impurity orbital. ComCTQMC can solve complex-valued impurities with crystal fields that are hybridized to both fermionic and bosonic baths. Most importantly, ComCTQMC utilizes graphical processing units (GPUs), if available, to dramatically accelerate the CTQMC algorithm when the Hilbert space is sufficiently large. We demonstrate acceleration by a factor of over 600 (100) in a simulation of δ-Pu at 600 K with (without) crystal fields. In easier problems, the GPU offers less impressive acceleration or even decelerates the CTQMC. Here we describe the theory, algorithms, and structure used by ComCTQMC in order to achieve this set of features and level of acceleration. Program Title: ComCTQMC CPC Library link to program files:https://doi.org/10.17632/x2gzgm8njh.1 Licensing provisions: GPLv3 Programming language: C++/CUDA Nature of problem: In dynamical mean-field theory (DMFT), the computational bottleneck is the repeated solution of a quantum impurity problem [1]. The continuous-time quantum Monte-Carlo (CTQMC) algorithm has emerged as one of the most efficient methods for solving multiorbital impurity problems at moderate-to-high temperatures [2]. However, the low-temperature regime remains inaccessible, particularly for f-shell systems, and the measurement of two-particle correlation functions on an impurity adds a substantial computational burden. The bottleneck of the CTQMC solver is itself the computation of the local trace which includes the multiplication of many moderate-to-large sized matrices. The efficient solution of the impurity, measurement of the two-particle correlation functions, and acceleration of the trace computation are therefore critical. Solution method: ComCTQMC uses the hybridisation expansion of the impurity action to explore partition space [3]. It uses the worm algorithm [4] to explore the union of the partition space with observables spaces, e.g., the two-particle correlat