A multi-orbital iterated perturbation theory for model Hamiltonians and real material-specific calculations of correlated systems

Abstract

Perturbative schemes utilizing a spectral moment expansion are well known and extensively used for investigating the physics of model Hamiltonians and real material systems. The advantages they offer, in terms of being computationally inexpensive, with real frequency output at zero and finite temperatures, compensate for their deficiencies and offer a quick, qualitative analysis of the system behavior. In this work, we have developed a method, that can be classified as a multi-orbital iterative perturbation theory (MO-IPT) to study N-fold degenerate and non degenerate Anderson impurity models. As applications of the solver, we have combined the method with dynamical mean field theory to explore lattice models like the single orbital Hubbard model, covalent band insulator and the multi-orbital Hubbard model for density-density type interactions in different parameter regimes. The Hund's coupling effects in case of multiple orbitals is also studied. The limitations and quality of results are gauged through extensive comparison with data from the numerically exact continuous time quantum Monte Carlo method (hybridization expansion CTQMC). In general we observe that the agreement with CTQMC results gets better as we move away from particle-hole symmetry. We have integrated MO-IPT with density functional theory based electronic structure methods to study real material systems. As a test case, we have studied the classic, strongly correlated electronic material, SrVO${}_3$. A comparison of density of states and photo emission spectrum (PES) with results obtained from different impurity solvers and experiments yields good agreement.

20 pages, 20 figures

References in corpus (25)

• Continuous-time Monte Carlo methods for quantum impurity models
• The numerical renormalization group method for quantum impurity systems
• Calculations of Hubbard U from first-principles
• Plane-wave based electronic structure calculations for correlated materials using dynamical mean-field theory and projected local orbitals
• High-spin to low-spin and orbital polarization transitions in multiorbital Mott systems
• Dynamical mean-field theory using Wannier functions: a flexible route to electronic structure calculations of strongly correlated materials
• Hund's coupling key role in multi-orbital correlations
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• First order character and observable signatures of topological quantum phase transitions
• Conserved quantities of SU(2)-invariant interactions for correlated fermions and the advantages for quantum Monte Carlo simulations
• Dynamical behavior across the Mott transition of two bands with different bandwidths
• Orbital-selective Mott-Hubbard transition in the two-band Hubbard model
• Efficient implementation of the continuous-time hybridization expansion quantum impurity solver
• Effect of Crystal-Field Splitting and Inter-Band Hybridization on the Metal-Insulator Transitions of Strongly Correlated Systems
• Temperature dependent correlations in covalent insulators
• Correlations in a band insulator
• Density functional plus dynamical mean field theory of the metal-insulator transition in early transition metal oxides
• Electronic structure and effects of dynamical electron correlation in ferromagnetic bcc-Fe, fcc-Ni and antiferromagnetic NiO
• Quantum Phase Transitions Between a Class of Symmetry Protected Topological States
• Role of rotational symmetry in the magnetism of a multiorbital model
• Sum rule violation in self-consistent hybridization expansions
• A local moment approach to the degenerate Anderson impurity model
• Finite-temperature phase transitions in the ionic Hubbard model
• Periodic Anderson model with electron-phonon correlated conduction band
• Interpolative Approach for Solving Quantum Impurity Model Based on the Slave--Boson Mean--Field Approximation

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