Itinerant ferromagnetism and polarons in SU(N) Fermi gases
(English) This thesis presents an in-depth study of the magnetic properties of repulsive Fermi gases in the continuum. Once a purely academic subject, Fermi gases can now be realized experimentally in ultracold atom laboratories, making a theoretical understanding of their behavior both timely and n...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:dnet:upcommonspor::63b472b8221cdc8802a4132ad5aa9a3b |
| Acceso en línea: | https://hdl.handle.net/2117/461058 https://dx.doi.org/10.5821/dissertation-2117-461058 |
| Access Level: | acceso abierto |
| Palabra clave: | Gasos de Fermi diluïts Ferromagnetisme itinerant Teoria de pertorbacions Sistemes SU(N) Polaró de Fermi 53 - Física Àrees temàtiques de la UPC::Física |
| Sumario: | (English) This thesis presents an in-depth study of the magnetic properties of repulsive Fermi gases in the continuum. Once a purely academic subject, Fermi gases can now be realized experimentally in ultracold atom laboratories, making a theoretical understanding of their behavior both timely and necessary. Our analysis focuses primarily on whether such systems favor a transition to a ferromagnetic state or remain paramagnetic. As technique, we use a perturbative approach that systematically includes the effects of higher-order terms, temperature, and mass imbalance. In the final part of the thesis, we also study the Fermi polaron problem. First, we examine a simple case: a Fermi gas with equal masses at zero temperature up to second order in perturbation theory. As this chapter can be considered an introduction to the magnetic phenomenology of Fermi gases, we compare the outcome of our second order analysis with the well-known scenario of the Stoner model, which is the first-order model. In both cases, a ferromagnetic transition always occurs. Moving from the Stoner model to the second-order one, there are two differences to point out: the continuous phase transition observed at S=1/2 becomes discontinuous, and the ferromagnetic phase arises at lower densities. The next step is to improve the description of the potential interaction. We do so by going up to third order in perturbation theory. However, this improvement comes with a cost; as we now have more information about the potential, the complexity of the problem is higher. We split the analysis into two parts. We first consider a hard-sphere potential without p-wave intra-particle interaction. We observe the same tendencies that we encounter when we move from first order to second order, but, more importantly, we recover the continuous phase transition for S=1/2. Having now at hand the third-order energies, we explore a wide range of different potentials. Surprisingly, for each spin S we observe a richness of scenarios: continuous transitions, discontinuous ones, combinations of the other two, stairs-like cases, and even, no transition at all. Next, we introduce another variable to our problem: the temperature. Thermal effects do not eliminate the ferromagnetic phase for any potential, but they clearly go against it: either they force the system to remain paramagnetic or make the transition to occur at higher densities, which probably hinders the ferromagnetic phase. Nevertheless, larger spins better resist these thermal effects. Additionally, temperature reduces the diversity of magnetic behavior, leading to more universal patterns: continuous transitions for S=1/2 and discontinuous ones for larger spins. Up to this point, we assumed that all the particles have the same mass. The next step is to consider different relations of masses. Adding another variable increases even more the complexity of the problem and, hence, we only inspect it at second order and at zero temperature. As we have commented above, at second order there is always a ferromagnetic transition. Now, this is also the case, but with some nuances. The massive particles are always the promoted ones, even at low densities. For S=1/2, this is the end of the story. But for larger spins, as we can have many mass relations, we can obtain lots of configurations, which may give us more tunability. Finally, we move beyond magnetic properties to study the Fermi polaron problem: an impurity immersed in a Fermi sea. We focus on how impurities affect our system. We examine the main properties of the Fermi polaron at third order and the effects of mass. Specifically, the massive polaron works just fine, but the light polaron is unstable. Altogether, this work offers a detailed and thorough exploration of Fermi gases, providing both qualitative insight and quantitative predictions relevant to experimental efforts. |
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