A wide variety of phenomena in condensed matter systems is driven primarily by interactions between electrons in the system. This work is concerned with the application of functional renormalization group (fRG) as a generalized solver for the multi-band Hamiltonians that describe these systems. We consider a decoupled formulation of the fRG equations that is optimized in the frequency and momentum domains and retains the flow of relevant modes in the system. Approximate truncations that extend the scheme to arbitrary multiband systems are addressed. This optimized decoupling is then used to derive the flow equations that describe fluctuations in model Hamiltonians for Cuprate and Pnictide superconductors. We construct a full phase diagram of the systems studied as a function of doping, temperature and coupling. Access to the frequency modes in the system allows us to explore the impact of coupling phonons to these model Hamiltonians. Alterations to the diagram due to electron-phonon coupling is derived. The results of the decoupled formulation is in agreement with results in the literature for many of the models considered. Further the fRG captures the sensitivity of susceptibilities of Cuprate Hamiltonians to band structure, the enhanced role of Hunds coupling in Pnictide systems and the impact of phonons in multiband Hamiltonians.
| Identifer | oai:union.ndltd.org:bu.edu/oai:open.bu.edu:2144/43991 |
| Date | 07 March 2022 |
| Creators | Yirga, Nahom K. |
| Contributors | Campbell, David K. |
| Source Sets | Boston University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
| Rights | Attribution 4.0 International, http://creativecommons.org/licenses/by/4.0/ |
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