Niggemann, Nils Frederic: Investigation of Quantum Spin Systems with Auxiliary Particles. , Dissertation, Berlin, Freie Universität Berlin, 2024
Open Access Version
Abstract:
This thesis presents advances in the description of quantum magnets, primarily through the development of a new method called the pseudo-Majorana functional renormalization group (PMFRG). The PMFRG is capable of accurately describing strongly interacting quantum magnets in challenging scenarios where most other methods fail. Fundamental to the formalism of the PMFRG is a resummation of Feynman diagrams, which allows direct treatment of the many-body problem in the ther- modynamic limit of infinitely many particles. While exact resummation schemes are impossible, the PMFRG uses the framework of the renormalization group to perform a numerical summation of several classes of diagrams to infinite order. Notable examples of such diagrams are associated with common phenomena such as magnetic order, as well as more exotic quantum spin liquids, which are phases described by emergent gauge theories and fractionalization. To exploit this advan- tage, spin operators for which diagrammatic techniques are limited are mapped to auxiliary Majorana fermions. This mapping proves to be advantageous compared to the more commonly used complex fermions. After establishing its formalism, the PMFRG is applied to paradigmatic problems in the field of frustrated mag- netism at finite temperature. The numerical results obtained with the PMFRG are shown to be quantitatively accurate, typically providing errors of less than 10% compared to exact solutions. In particular, the PMFRG remains applicable to more general scenarios of frustrated three-dimensional magnets where exact so- lutions are unavailable, and where most other methods are infeasible. In addition, this thesis investigates emergent higher-rank gauge theories with immobile quasiparticle excitations known as fractons. The physics of several pinch point features associated with these gauge theories is then analyzed. Using the PMFRG, it is found that these phases are very fragile under the inclusion of quan- tum fluctuations. Finally, a new fracton spin model is constructed that exhibits an exactly soluble point with a spin liquid phase. The stability of this phase is then verified by numerically exact quantum Monte Carlo simulations of the spin model compared to the analytical solution of the emergent rank-2 lattice gauge theory, making it the first two-body spin model with an emergent fracton quantum spin liquid. The following chapters therefore present substantial progress in two important areas: numerical solutions of the quantum many-body problem and the study of emergent gauge theories in spin systems.