Description du sujet de thèse

The thesis work will be an investigation into the role of generalized symmetries in condensed matter physics along two main axes:

1. Altermagnetism, topology and spin symmetries. This project is intended to explore the consequences of spin-space symmetries in condensed matter physics. Spin symmetries are generalizations of magnetic symmetries that are central to describe magnetic phases of matter at weak spin-orbit coupling. For example, they underlie altermagnetism - a topic of great current interest among condensed matter physicists. Recently we have adapted Landau theory to altermagnetism [1], which has shed light on the underlying altermagnetic order parameters, provided a spin symmetry based classification of these systems and supplied a predictive tool to guide experimental work in this area [2]. We have also done work exploring the fundamental group theory of these enlarged symmetries of which altermagnetic groups form a subset of all possible spin groups [3]. For this PhD project, our focus will be on how spin symmetries affect the topology of band structures including magnon bands and the implications of these symmetries for strongly interacting quantum matter. Though the project is primarily theoretical, there will be opportunities to collaborate with experimentalists working on altermagnetic materials and topological magnons.
2. Generalized symmetries, lattice gauge theories and quantum spin liquids. The phrase ``generalized symmetries'' often refers to, for example, higher form and non-invertible symmetries, which have profound implications in condensed matter and high-energy physics. In this project, we shall mainly be investigating lattice gauge theories coupled to scalar matter both in the deconfined regime and in the Higgs regime. Recent work has highlighted connections between symmetry protected topological phases and the Higgs regime in limiting cases where part of the protecting symmetry is a higher form symmetry [4]. This picture is cleanly applicable to Z2 and U(1) gauge theories. For non-Abelian gauge theories, the situation is more puzzling with certain signs indicating that there are strong parallels with the better-understood cases [5]. A key question motivating this work is whether one can generalize the SPT-Higgs picture to all gauge theories. More broadly, we investigate the generalized symmetries and their implications across the phase diagram of the theory including deconfined phases. This work is connected to various concrete condensed matter inspired systems notably quantum spin liquids in which gauge theories are emergent at low energies.



Mots clés – Keywords : Altermagnetism, Gauge theories, Representation theory, Spin liquids

[1] McClarty and Rau, Landau theory of altermagnetism Phys. Rev. Lett. 132, 176702 (2024)
[2] Schiff, McClarty, Rau, Romhányi, Collinear Altermagnets and their Landau Theories arXiv:2412.18025
[3] Schiff, Corticelli, Guerreiro, Romhányi, McClarty The crystallographic spin point groups and their representations Scipost Physics 18,109 (2025)
[4] Verresen, Borla, Vishwanath, Moroz, Thorngren, Higgs Condensates are Symmetry-Protected Topological Phases: I. Discrete Symmetries arXiv:2211.01376; Thorngren, Rakovszky, Verresen, Vishwanath, Higgs Condensates are Symmetry-Protected Topological Phases: II. U(1) Gauge Theory and Superconductors, arXiv:2303.08136
[5] Chung, Flores-Calderón, Torres, Ribeiro, Moroz, McClarty, Higgs Phases and Boundary Criticality, arXiv:2404.17001

Contexte de travail

Altermagnetism is one of the most rapidly progressing areas of modern condensed matter physics. For a review see Phys. Rev. X 12,040501. At the heart of the phenomenon is the set of magneto-crystalline symmetries at zero spin-orbit coupling. These are the spinsymmetries. These are weakly broken in real altermagnetic materials but a separation of energy scales ensures that they neverthelessdetermine the gross properties of weak spin-orbit coupled matter. At LLB we have an active group exploring the physics of these systemsboth on the theoretical and experimental sides.
Generalized symmetries have captured the imagination of theorists across multiple fi elds as they provide a new, deeper perspective onestablished physics such as phases of gauge theories and lead to multiple avenues for new physics. For a recent review see:https://www.annualreviews.org/content/journals/10.1146/annurev-conmatphys-040721-021029

Expected enrolment in the local doctoral school EDPIF with the doctoral training this entails on top of the core research project.
Standard PhD student salary and laboratory and computing facilities

Contraintes et risques

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