Accelerated impurity solver for DMFT and its diagrammatic extensions

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.

arXiv comment49 pages, 19 figures, submitted to Computer Physics Communications

References in corpus (28)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Continuous-time Monte Carlo methods for quantum impurity models
• The numerical renormalization group method for quantum impurity systems
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• Quantum Monte Carlo Impurity Solver for Cluster DMFT and Electronic Structure Calculations in Adjustable Base
• Dynamical Mean-Field Theory within the Full-Potential Methods: Electronic structure of Ce-115 materials
• What is the valence of a correlated solid? The double life of delta-plutonium
• TRIQS/CTHYB: A Continuous-Time Quantum Monte Carlo Hybridization Expansion Solver for Quantum Impurity Problems
• Modelling the Localized to Itinerant Electronic Transition in the Heavy Fermion System CeIrIn5
• Orthogonal Polynomial Representation of Imaginary-Time Green's Functions
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• Improved Estimators for the Self-Energy and Vertex Function in Hybridization Expansion Continuous-Time Quantum Monte Carlo Simulations
• $i$QIST: An open source continuous-time quantum Monte Carlo impurity solver toolkit
• Spectral Properties of delta-Plutonium: Sensitivity to 5f Occupancy
• Worm Improved Estimators in Continuous-time Quantum Monte Carlo
• Continuous-time Quantum Monte Carlo using Worm Sampling
• Continuous-time hybridization expansion quantum impurity solver for multi-orbital systems with complex hybridizations
• Krylov implementation of the hybridization expansion impurity solver and application to 5-orbital models
• ComDMFT: a Massively Parallel Computer Package for the Electronic Structure of Correlated-Electron Systems
• Lazy skip lists, a new algorithm for fast hybridization-expansion quantum Monte Carlo
• Importance of subleading corrections for the Mott critical point
• Continuous-time quantum Monte Carlo calculation of multi-orbital vertex asymptotics
• Negative sign problem in continuous-time quantum Monte Carlo: optimal choice of single-particle basis for impurity problems
• Ergodicity of the Hybridization-Expansion Monte Carlo Algorithm for Broken-Symmetry States
• Electronic Correlation Induced Expansion of Compensated Electron and Hole Fermi Pockets in delta-Plutonium
• Hybridization expansion Monte Carlo simulation of multi-orbital quantum impurity problems: matrix product formalism and improved Monte Carlo sampling
• Variational exact diagonalization method for Anderson impurity models

Cited by in corpus (9)

• Quenched pair breaking by interlayer correlations as a key to superconductivity in La${}_3$Ni${}_2$O${}_7$
• Photo-induced nonequilibrium states in Mott insulators
• Orbital Selective Mott Transition Effects and Non-Trivial Topology of Iron Chalcogenide
• Accuracy of ghost-rotationally-invariant slave-boson theory for multiorbital Hubbard models and realistic materials
• $\text{Ab initio}$ dynamical mean-field theory with natural orbitals renormalization group impurity solver: Formalism and applications
• Superconductivity in the two-dimensional Hubbard model with cellular dynamical mean-field theory: a quantum impurity model analysis
• Electronic correlations in epitaxial graphene: Mott states proximitized to a relativistic electron gas
• Real-Space Switching of Local Moments Driven by Quantum Geometry in Correlated Graphene Heterostructures
• Site-polarized Mott phases competing with a correlated metal in twisted WSe${}_2$