Mott insulators and the doping-induced Mott transition within DMFT: exact results for the one-band Hubbard model

Abstract

The paramagnetic phase of the one-band Hubbard model is studied at zero-temperature, within the framework of dynamical mean-field theory, and for general particle-hole asymmetry where a doping-induced Mott transition occurs. Our primary focus is the Mott insulator (MI) phase, and our main aim to establish what can be shown exactly about it. To handle the locally doubly-degenerate MI requires two distinct self-energies, which reflect the broken symmetry nature of the phase and together determine the standard single self-energy. Exact results are obtained for the local charge, local magnetic moment and associated spin susceptibilities, the interaction-renormalised levels, and the low-energy behaviour of the self-energy in the MI phase. The metallic phase is also considered briefly, and shown to acquire an emergent particle-hole symmetry as the Mott transition is approached. Throughout the metal, Luttinger's theorem is reflected in the vanishing of the Luttinger integral; for the generic MI by contrast this is shown to be non-vanishing, but again to have a universal magnitude. Numerical results are also obtained using NRG, for the metal/MI phase boundary, the scaling behaviour of the charge as the Mott transition is aproached from the metal, and associated universal scaling of single-particle dynamics as the low-energy Kondo scale vanishes.

15 pages, 8 figures

References in corpus (10)

• The numerical renormalization group method for quantum impurity systems
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• How bad metals turn good: spectroscopic signatures of resilient quasiparticles
• Bad-metal behavior reveals Mott quantum criticality in doped Hubbard models
• Breakdown of Luttinger's theorem in two-orbital Mott insulators
• Common non-Fermi liquid phases in quantum impurity physics
• Anderson impurity in a semiconductor
• Mott transition in the Hubbard model away from particle-hole symmetry
• A local moment approach to the degenerate Anderson impurity model

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• Luttinger's theorem in presence of Luttinger surfaces
• Necessary and Sufficient Conditions for the Validity of Luttinger's Theorem
• The Mott transition as a topological phase transition
• A local theory for Mott-Anderson localization
• Quantum critical local spin dynamics near the Mott metal-insulator transition in infinite dimensions
• Quantum critical Mott transitions in a bilayer Kondo insulator-metal model system
• Near room-temperature ferromagnetism from double-exchange in the van der Waals material CrGeTe${}_3$: evidence from optical conductivity under pressure
• Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model
• Emergent soft-gap Anderson models at quantum criticality in a lattice Hamiltonian within dynamical mean field theory
• Kondo frustration via charge fluctuations: a route to Mott localisation
• Long-term memory magnetic correlations in the Hubbard model: A dynamical mean-field theory analysis
• Strongly correlated Josephson junction: proximity effect in the single-layer Hubbard model