Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint

Abstract

We analyze the highly non-perturbative regime surrounding the Mott-Hubbard metal-to-insulator transition (MIT) by means of dynamical mean field theory calculations at the two-particle level. By extending the results of Schäfer, et al. [Phys. Rev. Lett. 110, 246405 (2013)] we show the existence of infinitely many lines in the phase diagram of the Hubbard model where the local Bethe-Salpeter equations, and the related irreducible vertex functions, become singular in the charge as well as the particle-particle channel. These divergence lines accumulate around the critical Mott endpoint in accordance with the interpretation as precursors of the MIT. By comparing our numerical data with analytical calculations of increasing complexity, such as for the disordered Binary Mixture and Falicov-Kimball (FK) models, as well as for the atomic limit (AL) case, (i) we identify two different kinds of divergences lines; (ii) we classify them in terms of the frequency-structure of the associated singular eigenvectors; (iii) we investigate their relation to the multiple branches in the Luttinger-Ward formalism. Moreover, we could distinguish the situations where the multiple divergences simply reflect the emergence of an underlying, unique energy scale ${\nu }^{\ast }$ below which perturbation theory does no longer apply, from those where the breakdown of perturbation theory affects, not trivially, different energy regimes. Finally, we discuss the implications of our results on the theoretical understanding of the non-perturbative physics around the MIT and for future developments of many-body algorithms applicable in this regime.

28 pages, 15 figures

References in corpus (17)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Continuous-time Monte Carlo methods for quantum impurity models
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Spin freezing transition and non-Fermi-liquid self-energy in a 3-orbital model
• Kinks in the dispersion of strongly correlated electrons
• 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
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• Influence of Spatial Correlations in Strongly Correlated Electron Systems: Extension to Dynamical Mean Field Approximation
• Conserved quantities of SU(2)-invariant interactions for correlated fermions and the advantages for quantum Monte Carlo simulations
• Parquet decomposition calculations of the electronic self-energy
• Mott physics and collective modes: an atomic approximation of the four-particle irreducible functional
• Superperturbation solver for quantum impurity models
• Correlated starting points for the functional renormalization group
• Emergent Collective Modes and Kinks in Electronic Dispersions
• Kinks in the electronic specific heat
• Common non-Fermi liquid phases in quantum impurity physics

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