Many-body perturbation theory algorithm for multiband systems, Floquet Moiré materials and beyond

Assi, Ibsal A T (2023) Many-body perturbation theory algorithm for multiband systems, Floquet Moiré materials and beyond. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

In the first part of this work we introduce the symbolic determinant method (symDET) for constructing many-body perturbative expansions which is motivated by the Algorithmic Matsubara Integration (AMI) algorithm introduced recently [Taheridehkordi, A., Curnoe, S. H., & LeBlanc, J. P. F. PRB, 99(3), 035120, (2019)]. This algorithm is capable of performing both imaginary and real frequency calculations of physical observables at all coupling parameters, temperatures, etc., making it a promising tool for studying a variety of problems from lattice models to molecular chemistry problems. The current form of our symDET applies to both single and multiband systems with general two-body interactions, but it can be easily extended to beyond two-body interactions by the proper handling of Wick contractions. Although the computational expense increases for multiband problems at higher order perturbation theory, our algorithm is still parallelizable. Furthermore, optimizations still exist. One way could be by following the steps of the connected determinant method (cDET) [ R. Rossi, Phys. Rev. Lett. 119, 045701 (2017)] and the minimal determinant algorithms introduced recently [Šimkovic IV, F., & Ferrero, M. PRB, 105(12), 125104, (2022)]. As an illustration, we applied symDET to a variety of problems such as the hydrogen molecule with 2 and 10 bases, the Hubbard dimer model which is an effective 4 bands system, and the Hubbard model with an effective doubly degenerate band. In the second part of this thesis, we review the Floquet method which is used to study non-equilibrium systems. In particular, we focused on its application to twisted multilayered systems for which the appearance of flat bands at magic angles is a sign of interesting physical states, such as superconductivity which can observed experimentally in those systems. As an illustration, we applied this method to twisted bilayer and trilayer graphene systems. For the first example, we considered the twisted trilayer graphene (TTLG) system with different types of light applied vertically onto layers, mainly circularly polarized light and light from a waveguide, and we focused on the topological maps where we found that for the special case of ABC stacking, those maps are dependent on the handedness of the circularly polarized light. This dependence can be captured via optical conductivity measurements. Secondly, we studied the twisted bilayer graphene (TBLG), with the usual tight binding Hamiltonian together with interlayer hopping interactions, and then on top of that we included the Haldane interaction. The application of circularly polarized and waveguide lights were discussed where we considered the effects of light on the band structure of this model. For the Haldane TBLG we found that the band structure depends on the polarization of the incident light, something that was observed in the TTLG with ABC stacking but never seen in the usual TBLG system, hence we owe that to time reversal symmetry breaking. Lastly, we discuss the possible extensions of symDET to bosonic systems and the possible future application of symDET to twisted multilayer systems that has rich physics with a wide range of applications.

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