Transport and diffusion of charge, spin, and heat in the two dimensional Hubbard model

Ulaga, Martin (author), Kokalj, Jure (mentor), Mravlje, Jernej (co-mentor)

This thesis addresses transport questions in strongly correlated electronic systems in two dimensions. The primary tool for the analysis is the exact numerical treatment of the problem on small clusters, which allows for a description of transport at high temperatures, combined with dynamical mean-field theory and phenomenological approaches. The high-temperature regime under consideration primarily concerns temperatures above the melting point of most materials, but is the natural operating grounds of quantum simulators based on cold atomic gases in optical lattices. We calculate the spin diffusion constant at high temperatures and compare the results with just such an experiment, reproducing the disagreement between theory and experiment in the process. As a possible cause for this discrepancy, we study the spin thermoelectric effect and find it is enhanced in the presence of strong correlations, leading to the mixing of spin and heat transport. We also calculate the ordinary thermoelectric effect and estimate its contribution to the transport of heat. We evaluate the ratio between heat and charge conductivity which at the lowest reachable temperatures indicates the restoration of the Wiedemann-Franz law in the strongly correlated system. We develop a theoretical framework for estimating the influence of the thermoelectric effect on a diffusion experiment following a quench in a quantum simulator and observe the development of an additional long timescale.

• Language: English
• Keywords: electronic correlations, Hubbard model, Heisenberg model, transport, bad metal, spin bad metal, spin diffusion, heat diffusion, thermoelectric effect, Lorenz number.
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2024
• PID: 20.500.12556/RUL-153547
• COBISS.SI-ID: 183812355
• Publication date in RUL: 14.01.2024

Secondary language

• Language: Slovenian
• Title: Transport in difuzija naboja, spina in toplote v dvodimenzionalnem Hubbardovem modelu

Abstract

To doktorsko delo naslavlja vprašanja transporta v močno koreliranih elektronskih sistemih v dveh dimenzijah. Poglavitno orodje za ta namen je točna numerična obravnava problema na majhnih sistemih, kar omogoča opis transporta pri visokih temperaturah, v kombinaciji z dinamično teorijo povprečnega polja in fenomenološkimi pristopi. Obravnavan visokotemperaturni režim sicer primarno zadeva temperature, ki presegajo tališče večine snovi, vendar v njem naravno operirajo kvantni simulatorji na osnovi atomskih plinov v optični rešetki. Pri visoki temperaturi izračunamo spinsko difuzijsko konstanto in jo primerjamo s prav takim eksperimentom, pri čemer reproduciramo nestrinjanje med teorijo in eksperimentom. Kot možen vzrok za odstopanje preučimo spinski termoelektrični pojav, ki je močno ojačan zaradi prisotnosti močnih interakcij in vodi do mešanja spinske in toplotne difuzije. Izvrednotimo tudi običajni termoelektrični pojav in ocenimo njegov prispevek k transportu toplote. Izračunamo razmerje med toplotno in običajno prevodnostjo, ki se pri najnižjih dosegljivih temperaturah približuje skladnosti z zakonom Wiedemanna in Franza v močno koreliranem sistemu. Razvijemo tudi teoretsko ogrodje za obravnavo vpliva termoelektričnega pojava na difuzijski poskus s kaljenjem v kvantnem simulatorju in opazimo razvoj dodatne počasne časovne skale.

• Keywords: elektronske korelacije, Hubbardov model, Heisenbergov model, transport, slaba kovina, spinska slaba kovina, spinska difuzija, toplotna difuzija, termoelektrični pojav, Lorenzovo število.