Accelerated impurity solver for DMFT and its diagrammatic extensions

• Main Authors: Melnick, Corey, Sémon, Patrick, Yu, Kwangmin, D'Imperio, Nicholas, Tremblay, André-Marie, Kotliar, Gabriel
• Format: Journal Article
• Language: English
• Published: 16-10-2020
• Subjects: Physics - Strongly Correlated Electrons
• DOI: 10.48550/arxiv.2010.08482

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.