Truncated Configuration Interaction expansions as solvers for correlated quantum impurity models and dynamical mean field theory

Abstract

The development of polynomial cost solvers for correlated quantum impurity models, with controllable errors, is a central challenge in quantum many-body physics, where these models find applications ranging from nano-science to the dynamical mean-field theory (DMFT). Here we describe how configuration interaction (CI) approximations to exact diagonalization (ED) may be used as solvers in DMFT. CI approximations retain the main advantages of ED, such as the ability to treat general interactions and off-diagonal hybridizations and to obtain real spectral information, but are of polynomial cost. Furthermore, their errors can be controlled by monitoring the convergence of physical quantities as a function of the CI hierarchy. Using benchmark DMFT applications, such as single-site DMFT of the 1D Hubbard model and $2\times 2$ cluster DMFT of the 2D Hubbard model, we show that CI approximations allow us to obtain near-exact ED results for a tiny fraction of the cost. This is true over the entire range of interaction strengths including "difficult" regimes, such as in the pseudogap phase of the 2D Hubbard model. We use the ability of CI approximations to treat large numbers of orbitals to demonstrate convergence of the bath representation in the $2\times 2$ cluster DMFT using a 24 bath orbital representation. CI approximations thus form a promising route to extend ED to problems that are currently difficult to study using other solvers such as continuous-time quantum Monte Carlo, including impurity models with large numbers of orbitals and general interactions.

References in corpus (30)

• Spins in few-electron quantum dots
• 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
• Quantum Cluster Theories
• A continuous-time solver for quantum impurity models
• Continuous Time Quantum Monte Carlo method for fermions
• Cellular Dynamical Mean Field Approach to 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
• Antiferromagnetism and d-wave superconductivity in cuprates: a uster DMFT study
• Janus-faced influence of the Hund's rule coupling in strongly correlated materials
• Cluster Dynamical Mean Field Theory of the Mott Transition
• Numerical Renormalization Group Calculations for the Self-energy of the impurity Anderson model
• Spin freezing transition and non-Fermi-liquid self-energy in a 3-orbital model
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• Dynamical Breakup of the Fermi Surface in a doped Mott Insulator
• Anomalous superconductivity and its competition with antiferromagnetism in doped Mott insulators
• Dynamical mean-field theory from a quantum chemical perspective
• Dynamical Mean Field Theory with the Density Matrix Renormalization Group
• Sum-rules and bath-parametrization for quantum cluster theories
• Finite doping signatures of the Mott transition in the two-dimensional Hubbard model
• Local Order and the gapped phase of the Hubbard model: a plaquette dynamical mean field investigation
• Temperature and bath size in exact diagonalization dynamical mean field theory
• Metal-Insulator phase diagram and orbital selectivity in 3-orbital models with rotationally invariant Hund coupling
• A new numerical algorithm for the double-orbital Hubbard model -- Hund-coupled pairing symmetry in the doped case
• Bath optimization in the Cellular Dynamical Mean Field Theory
• Multisite versus multiorbital Coulomb correlations studied within finite-temperature exact diagonalization dynamical mean-field theory
• Quantum Monte Carlo study for multiorbital systems with preserved spin and orbital rotational symmetries
• Quantum Impurity Problems in Condensed Matter Physics

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