Lazy skip lists, a new algorithm for fast hybridization-expansion quantum Monte Carlo

Abstract

The solution of a generalized impurity model lies at the heart of electronic structure calculations with dynamical mean-field theory (DMFT). In the strongly-correlated regime, the method of choice for solving the impurity model is the hybridization expansion continuous time quantum Monte Carlo(CT-HYB). Enhancements to the CT-HYB algorithm are critical for bringing new physical regimes within reach of current computational power. Taking advantage of the fact that the bottleneck in the algorithm is a product of hundreds of matrices, we present optimizations based on the introduction and combination of two concepts of more general applicability: a) skip lists and b) fast rejection of proposed configurations based on matrix bounds. Considering two very different test cases with $d$ electrons, we find speedups of $\sim 25$ up to $\sim 500$ compared to the direct evaluation of the matrix product. Even larger speedups are likely with $f$ electron systems and with clusters of correlated atoms.

Latex,10 pages, 6 figures. More extensive references and comments

References in corpus (13)

• Continuous-time Monte Carlo methods for quantum impurity models
• The ALPS project release 1.3: open source software for strongly correlated systems
• Quantum Monte Carlo Impurity Solver for Cluster DMFT and Electronic Structure Calculations in Adjustable Base
• Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
• Cluster Dynamical Mean Field Theory of the Mott Transition
• Strongly Correlated Superconductivity: a plaquette Dynamical mean field theory study
• Finite doping signatures of the Mott transition in the two-dimensional Hubbard model
• Site-Selective Electronic Correlation in alpha-Plutonium Metal
• c-axis resistivity, pseudogap, superconductivity and Widom line in doped Mott insulators
• Importance of many body effects in the kernel of hemoglobin for ligand binding
• Avoided Quantum Criticality near Optimally Doped High Temperature Superconductors
• Ergodicity of the Hybridization-Expansion Monte Carlo Algorithm for Broken-Symmetry States
• Hybridization expansion Monte Carlo simulation of multi-orbital quantum impurity problems: matrix product formalism and improved Monte Carlo sampling

Cited by in corpus (34)

• TRIQS/CTHYB: A Continuous-Time Quantum Monte Carlo Hybridization Expansion Solver for Quantum Impurity Problems
• Bad metallic transport in a cold atom Fermi-Hubbard system
• Applications of DFT+DMFT in Materials Science
• $i$QIST: An open source continuous-time quantum Monte Carlo impurity solver toolkit
• An organizing principle for two-dimensional strongly correlated superconductivity
• Electronic structure of cerium: A comprehensive first-principles study
• Entanglement entropy and mutual information across the Mott transition in the two-dimensional Hubbard model
• Continuous-time hybridization expansion quantum impurity solver for multi-orbital systems with complex hybridizations
• Thermodynamic and information-theoretic description of the Mott transition in the two-dimensional Hubbard model
• Nature of the 5$f$ electronic structure of plutonium
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Antagonistic effects of nearest-neighbor repulsion on the superconducting pairing dynamics in the doped Mott insulator regime
• Effects of interaction strength, doping, and frustration on the antiferromagnetic phase of the two-dimensional Hubbard model
• Pressure-driven 4$f$ localized-itinerant crossover in heavy fermion compound CeIn${}_3$: A first-principles many-body perspective
• State- and superstate-sampling in hybridization-expansion continuous-time quantum Monte Carlo
• Emergence of quasiparticle multiplets in curium
• Molecular Mott state in the deficient spinel GaV${}_4$S${}_8$
• Topological Phase Transition in an Archetypal f-electron Correlated System: Ce
• Pressure-Driven 5$f$ Localized-Itinerant Transition and Valence Fluctuation in Californium
• Entanglement and classical correlations at the doping-driven Mott transition in the two-dimensional Hubbard model
• Accelerated impurity solver for DMFT and its diagrammatic extensions
• Validity of the Local Approximation in Iron- Pnictides and Chalcogenides
• Information-theoretic measures of superconductivity in a two-dimensional doped Mott insulator
• Prediction of anomalies in the velocity of sound for the pseudogap of hole-doped cuprates
• A "hidden" transition in heavy fermion compound CeB${}_6$ at $T\sim$ 20 K?
• $\text{Ab initio}$ 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
• Ambipolar doping of a charge-transfer insulator in the Emery model
• An investigation of the interrelationship between pressure and correlation in LaFeAsO under pressure
• Charge gap and charge redistribution among copper and oxygen orbitals in the normal state of the Emery model
• Crystalline anisotropy induces a second antiferromagnetic phase in the absence of SDW in the heavily hydrogen-doped LaFeAsO${}_{1-x}$H${}_x$ $(x\sim 0.5)$
• Dynamics of superconducting pairs in the two-dimensional Hubbard model
• The Frenkel line and the pseudogap: an analogy between classical and electronic fluids
• Improvement of the simplification method for the local two-particle full-vertex towards precise frequency behavior