Pseudoparticle vertex solver for quantum impurity models
arXiv:2204.13562 · doi:10.1103/PhysRevB.106.085124
Abstract
We present a quantum impurity solver based on a pseudo-particle framework, which combines diagrammatic resummations for a three-point vertex with diagrammatic Monte Carlo sampling of a four-point vertex. This recently proposed approach [A. J. Kim et al., arXiv:2112.15549] is generalized here to fermionic impurity problems and we discuss the technical details of the implementation, including the time-stepping approach, the Monte Carlo updates, and the routines for checking the two-particle irreducibility of the four-point vertex. We also explain how the vertex information can be efficiently stored using a Dubiner basis representation. The convergence properties of the algorithm are demonstrated with applications to exactly solvable impurity models and dynamical mean field theory simulations of the single-orbital Hubbard model. It is furthermore shown that the algorithm can handle a two-orbital problem with off-diagonal hybridizations, which would cause a severe sign problem in standard hybridization-expansion Monte Carlo simulations. Since the vertex-based algorithm successfully handles sign oscillating integrals in equilibrium and samples only connected diagrams, it may be a promising approach for real-time simulations.
16 pages, 21 figures
References in corpus (16)
- Continuous-time Monte Carlo methods for quantum impurity models
- The numerical renormalization group method for quantum impurity systems
- Real-time path integral approach to nonequilibrium many-body quantum system
- Diagrammatic Monte Carlo simulation of non-equilibrium systems
- Spin Precession and Real Time Dynamics in the Kondo Model: A Time-Dependent Numerical Renormalization-Group Study
- Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
- Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
- Solving nonequilibrium dynamical mean-field theory using matrix product states
- Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
- Density matrix numerical renormalization group for non-Abelian symmetries
- Steady-state nonequilibrium density of states of driven strongly correlated lattice models in infinite dimensions
- On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime
- Currents and Green's functions of impurities out of equilibrium -- results from inchworm Quantum Monte Carlo
- J-freezing and Hund's rules in spin-orbit-coupled multiorbital Hubbard models
- Quantum Monte Carlo solution of the dynamical mean field equations in real time
- Estimate of the Phase Transition Line in the Infinite-dimensional Hubbard Model