Fermi-liquid theory and divergences of the two-particle irreducible vertex in the periodic Anderson lattice

Journal Article · Mon Apr 06 00:00:00 EDT 2020 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.101.165105· OSTI ID:1631022

Melnick, Corey ^[1]; Kotliar, Gabriel ^[2]

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1. Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics
2. Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics; Rutgers Univ., New Brunswick, NJ (United States)

Here we analyze the divergences of the irreducible vertex function in dynamical mean field theory, which may indicate either a nonphysical breakdown of the perturbation theory or a response to some physical phenomenon. To investigate this question, we construct a quasiparticle vertex from the diverging irreducible vertex functions. This vertex describes the scattering between quasiparticles and quasiholes in a Fermi liquid. We show that the quasparticle vertex does not diverge in the charge channel, wherein the irreducible vertex does diverge; and we show that the quasiparticle vertex does diverge in the spin channel, wherein the irreducible vertex does not diverge. This divergence occurs at the Mott transition, wherein the Fermi-liquid theory breaks down. Both the half filled Hubbard and Anderson lattices are investigated. In general, our results support that the divergences of the irreducible vertex function do not indicate a nonphysical failure of the perturbation theory. Instead, the divergences are the mathematical consequence of inverting a matrix (the local charge susceptibility) which accumulates increasingly negative diagonal elements as the Hubbard interaction suppresses charge fluctuations. Indeed, we find that the first divergences of the irreducible vertex in both Hubbard and Anderson lattices occurs near the maximum magnitude of the (negative) vertex-connected part of the charge susceptibility.

• Research Organization: Brookhaven National Laboratory (BNL), Upton, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0012704
• OSTI ID: 1631022
• Alternate ID(s): OSTI ID: 1608388
• Report Number(s): BNL--215943-2020-JAAM
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 16 Vol. 101; ISSN 2469-9950; ISSN PRBMDO
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Dynamical mean field theory
Electronic structure
Fermi liquid theory
Physical Systems
Strongly correlated systems