20.500.12556/RUL-138759 Model majhnega polarona - sklopitev elektronov z bozoni s trdo sredico Small polaron model - electrons coupled to hard-core bosons Elektron elektrostatsko interagira z okoliškimi gradniki kristalne rešetke polarizabilnega kristala. Kot posledica interakcije se okoli elektrona deformira rešetka in se tvori polaronski kompleks. Lastnosti polarona, kvazidelca elektron-fononske sklopitve, so precej drugačne od lastnosti prostega elektrona. Fizikalne lastnosti sistema, v katerem je omenjena interakcija prisotna, so lahko torej povsem drugačne kot lastnosti sistema, kjer je ta sklopitev zanemarljiva. Že kar nekaj časa je znano, da interakcija elektronov s fononi omogoča nastanek nizkotemperaturne superprevodnosti. Ni pa še povsem jasno, ali elektron-fononska sklopitev igra ključno vlogo tudi pri mehanizmu visokotemperaturnih superprevodnikov in pri kolosalni magnetoupornosti feromagnetnih oksidov. Magistrsko delo se posveča modelu majhnega polarona. Standardni Holstein-Hubbardov model omejimo z zamenjavo fononov z bozoni s trdo sredico (HCB). HCB model apliciramo na enodimenzionalni sistem enega oziroma dveh elektronov. Analiziramo statične lastnosti sistemov kot so energijska disperzija najnižjih stanj, pričakovano število bozonov v teh stanjih, kinetična energija, kvazidelčna teža in efektivna masa polarona, ter spektralno funkcijo. Obnašanje modela se zaradi omejitve trde sredice precej razlikuje od napovedi standardnega Holstein-Hubbardovega modela. Kljub temu pa je model še kako relavanten, saj se njegove prostostne stopnje ujemajo s prostostnimi stopnjami verige spinov-1/2 in posledično omogoča opis spinskih polaronov. V zaključku omenimo nekaj potencialnih smeri nadaljnega dela. An electron interacts electrostatically with the surrounding building blocks of a polarisable crystal lattice. The consequence of the interaction is a deformation formed around the electron. This complex is called a polaron, a quasiparticle of the electron-phonon interaction. Polaron properties are a lot different than the properties of a free electron. Physical properties of the system, in which such interaction is present, can, consequently, also be a lot different from the properties of a system, in which this interaction is negligible. It has been known for quite some time already that the interaction of electrons with phonons enables low-temperature superconductivity. However, it is still not certain whether it also plays an important role in the mechanism of the high-temperature superconductors and colossal magnetoresistance in ferromagnetic oxides. This work is dedicated to the small polaron model. We restrict the standard Holstein-Hubbard model by replacing phonons with hard-core bosons (HCB). We apply the HCB model to the one-dimensional one-electron and two-electron systems. We analyze the static properties such as the energy dispersion of the lowest-lying states, the expected number of bosons in these states, the kinetic energy, the quasiparticle weight, the polaron's effective mass, and also the spectral function. The behavior of the model is a lot different than the prediction of the standard Holstein-Hubbard model due to the restriction. Nevertheless, the model is quite relevant because its degrees of freedom match the degrees of freedom of the spin-1/2 system. In conclusion, we mention some of the potential directions for further work. polaroni elektron-fononska sklopitev Holstein-Hubbardov model bozoni s trdo sredico spektralna funkcija polarons electron-phonon coupling Holstein-Hubbard model hard-core bosons spectral function true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2022-08-16 11:15:24 2022-08-16 11:15:41 2026-06-08 11:58:52 0000-00-00 00:00:00 2022 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 123789 120201475 4453.pdf 4453.pdf 1 825BE64000A8B08D3F66671403F6FCAF 67dc91415ce9b6a47a45cb6b27c3b938ad2a62ec87bc8284a996171785e4af1c 03e35ae8-1d44-11ed-92af-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=159196 Fakulteta za matematiko in fiziko 0 0 0