Study of itinerant ferromagnetism and polarons in degenerate Fermi gases

Apr 20, 2026

Jordi Pera i Ferreruela defended his doctoral thesis co-directed by Joaquim Casulleras i Ambrós and Jordi Boronat Medico on April 17, 2026 at Campus Nord. The thesis, entitled Itinerant ferromagnetism and polarons in SU(N) Fermi gases, focuses on determining under which regimes Fermi gases become ferromagnetic and, if so, how they get there. On the other hand, it also includes a small exploration of the behavior of impurities in these gases.

Study of itinerant ferromagnetism and polarons in degenerate Fermi gases — Types of ferromagnetic phase transitions for spins S = 1/2, 3/2, 5/2, 7/2 and 9/2 (from top to bottom, and from left to right). The transitions depend on the effective range in s-wave, r0, and the dispersion length in p-wave, a1, which carry information about the potential. C means continuous, D discontinuous, CD continuous-discontinuous, and S scaled. If there is a P, then the transition is also partial. And NON means that there is no transition, so the gas remains paramagnetic. The temperature is assumed to be zero. We see that for S=1/2 the type of transition that dominates is the continuous one, while for S>1/2 it is the discontinuous one.

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 ultra-cold 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. The next step is to improve the description of the interaction, and so we extend the study to third order in perturbation theory, where we explore a wide range of potentials. Next, we introduce temperature as a new variable. The next step is to consider different mass ratios. Finally, we extend the study beyond magnetic properties to analyze the problem of the fermionic polaron, an impurity immersed in a Fermi sea.

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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