Accelerated impurity solver for DMFT and its diagrammatic extensions

TL;DR

ComCTQMC is a GPU-accelerated quantum impurity solver based on CTQMC, significantly speeding up calculations for complex impurity problems in DMFT and its extensions, with demonstrated acceleration factors over 600.

Contribution

The paper introduces ComCTQMC, a GPU-accelerated CTQMC impurity solver supporting complex impurities and various measurements, achieving substantial speedups for large Hilbert spaces.

Findings

Over 600x acceleration for complex impurity problems

Supports both fermionic and bosonic baths with crystal fields

Efficient measurement of Green's functions and observables

Abstract

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 $\delta$-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.