Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
| Autor: | Patrik Thunström, Sergio Ciuchi, Olle Gunnarsson, G. Rohringer |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Electronic
Optical and Magnetic Materials Condensed Matter Physics Physics Strongly Correlated Electrons (cond-mat.str-el) FOS: Physical sciences Atom (order theory) Vertex function Function (mathematics) Electron 01 natural sciences 010305 fluids & plasmas Vertex (geometry) Condensed Matter - Strongly Correlated Electrons Theoretical physics Simple (abstract algebra) 0103 physical sciences Electronic Particle Gravitational singularity Optical and Magnetic Materials 010306 general physics |
| Zdroj: | Physical Review B 98 (2018). doi:10.1103/PhysRevB.98.235107 info:cnr-pdr/source/autori:Thunstroem, P.; Gunnarsson, O.; Ciuchi, Sergio; Rohringer, G./titolo:Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom/doi:10.1103%2FPhysRevB.98.235107/rivista:Physical Review B/anno:2018/pagina_da:/pagina_a:/intervallo_pagine:/volume:98 |
| ISSN: | 2469-9969 2469-9950 |
| DOI: | 10.1103/physrevb.98.235107 |
| Popis: | Two-particle generalized susceptibilities and their irreducible vertex functions play a prominent role in the quantum many-body theory for correlated electron systems. They act as basic building blocks in the parquet formalism which provides a flexible scheme for the calculation of spectral and response functions. The irreducible vertices themselves have recently attracted increased attention as unexpected divergences in these functions have been identified. Remarkably, such singularities appear already for one of the simplest strongly interacting systems: the atomic limit of the half-filled Hubbard model (Hubbard atom). In this paper, we calculate the analytical expressions for all two-particle irreducible vertex functions of the Hubbard atom in all scattering channels as well as the fully irreducible two-particle vertices. We discuss their divergences and classify them by the eigenvalues and eigenvectors of the corresponding generalized susceptibilities. In order to establish a connection to the recently found multivaluedness of the exact self-energy functional $\Sigma[G]$, we show that already an approximation akin to iterated perturbation theory is sufficient to capture, qualitatively, the divergent structure of the vertex functions. Finally, we show that the localized divergences in the disordered binary mixture model are directly linked to a minimum in the single-particle Matsubara Green's function. Comment: 16 pages, 3 figures |
| Databáze: | OpenAIRE |
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