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.
arXiv comment16 pages, 21 figures
References in corpus (37)
- Continuous-time Monte Carlo methods for quantum impurity models
- The numerical renormalization group method for quantum impurity systems
- A continuous-time solver for quantum impurity models
- Nonequilibrium dynamical mean-field theory and its applications
- Continuous Time Quantum Monte Carlo method for fermions
- Real-time path integral approach to nonequilibrium many-body quantum system
- Polaron Problem by Diagrammatic Quantum Monte Carlo
- Diagrammatic Monte Carlo simulation of non-equilibrium systems
- Non-abelian symmetries in tensor networks: a quantum symmetry space approach
- Spin Precession and Real Time Dynamics in the Kondo Model: A Time-Dependent Numerical Renormalization-Group Study
- A New Iterative Perturbation Scheme for Lattice Models with Arbitrary Filling
- Taming the dynamical sign problem in real-time evolution of quantum many-body problems
- Nonequilibrium dynamical mean-field calculations based on the non-crossing approximation and its generalizations
- Diagrammatic Monte Carlo
- 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
- Interaction quench in the Hubbard model: Relaxation of the spectral function and the optical conductivity
- Anderson impurity model at finite Coulomb interaction U: generalized Non-crossing Approximation
- Diagrammatic Monte Carlo for Correlated Fermions
- Weak-coupling quantum Monte Carlo calculations on the Keldysh contour: theory and application to the current-voltage characteristics of the Anderson model
- Solving nonequilibrium dynamical mean-field theory using matrix product states
- Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
- Fork Tensor Product States - Efficient Three Orbital Real Time DMFT Solver
- 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
- Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
- Currents and Green's functions of impurities out of equilibrium -- results from inchworm Quantum Monte Carlo
- Generalized Wilson Chain for solving multichannel quantum impurity problems
- 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
- Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations
- Non-thermal melting of Neel order in the Hubbard model
- Exact Transformation for Spin-Charge Separation of Spin-half Fermions without Constraints
- Multi-valuedness of the Luttinger-Ward functional in the Fermionic and Bosonic System with Replicas
- Spin-charge transformation of lattice fermion models: duality approach for diagrammatic simulation of strongly correlated systems
- Estimate of the Phase Transition Line in the Infinite-dimensional Hubbard Model