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T. Schäfer, S. Ciuchi, M. Wallerberger, P. Thunström, O. Gunnarsson, G. Sangiovanni, G. Rohringer, A. Toschi:
"Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint";
Physical Review B, 94 (2016), 235108; 1 - 25.

We analyze the highly non-perturbative regime surrounding the
Mott-Hubbard metal-to-insulator transition (MIT) by means of dynamical
mean field theory (DMFT) 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. By comparing our numerical data for the Hubbard model
with analytical calculations for exactly solvable systems of increasing complexity [disordered binary mixture (BM), Falicov-Kimball (FK) and atomic limit (AL)],
we have (i) identified two different kinds of divergence lines; (ii) classified them in terms of the frequency-structure of the associated singular eigenvectors; (iii) investigated their relation to the emergence of multiple branches in the Luttinger-Ward functional.
In this way, we could distinguish the situations where the multiple divergences simply reflect the emergence
of an underlying, single energy scale v* below which perturbation theory is no longer applicable,
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.

vertex, divergences, dynamical mean field theory, Mott-Hubbard transition

http://dx.doi.org/10.1103/PhysRevB.94.235108

Project Head Alessandro Toschi:
Quantum criticality in strongly correlated magnets