Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions
| Autor: | Amir Taheridehkordi, James P.F. LeBlanc, Stephanie Curnoe |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Strongly Correlated Electrons (cond-mat.str-el)
Hubbard model Numerical analysis Analytic continuation FOS: Physical sciences Matsubara frequency 02 engineering and technology 021001 nanoscience & nanotechnology 01 natural sciences Square lattice Condensed Matter - Strongly Correlated Electrons Diagrammatic reasoning symbols.namesake 0103 physical sciences symbols Feynman diagram Statistical physics 010306 general physics 0210 nano-technology Graph property Mathematics |
| Zdroj: | Physical Review B. 102 |
| ISSN: | 2469-9969 2469-9950 |
| DOI: | 10.1103/physrevb.102.045115 |
| Popis: | We systematically generate the perturbative expansion for the two-particle spin susceptibility in the Feynman diagrammatic formalism and apply this expansion to a model system - the single-band Hubbard model on a square lattice. We make use of algorithmic Matsubara integration (AMI) [A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 99, 035120 (2019)] to analytically evaluate Matsubara frequency summations, allowing us to symbolically impose analytic continuation to the real frequency axis. We minimize our computational expense by applying graph invariant transformations [Amir Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 101, 125109 (2020)]. We highlight extensions of the random-phase approximation and T-matrix methods that, due to AMI, become tractable. We present results for weak interaction strength where the direct perturbative expansion is convergent, and verify our results on the Matsubara axis by comparison to other numerical methods. By examining the spin susceptibility as a function of real-frequency via an order-by-order expansion we can identify precisely what role higher order corrections play on spin susceptibility and demonstrate the utility and limitations of our approach. |
| Databáze: | OpenAIRE |
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