Thema der Dissertation:
Generalizations of Pseudo Majorana Functional Renormalization Group and its Application to Highly Frustrated Spin Systems
Generalizations of Pseudo Majorana Functional Renormalization Group and its Application to Highly Frustrated Spin Systems
Abstract: Spin systems are known for their purely interacting nature, causing them to lack the canonical perturbative limit of small kinetic energies, which would usually help to understand some of the fundamental physics. A method that has proven effective for the description of strongly correlated systems is functional renormalization group (FRG), which can be thought of as an alternative to the path integral formalism as an approach to many-body quantum mechanics. Formulating FRG in terms of spins turns out to be a subtle endeavor, though, as the spin algebra relations are relatively complicated compared to, for example, the canonical anti-commutation relations of fermions. One possible way to use the advantages of FRG for spin systems, is to map spins onto Majorana operators, leading to the so called pseudo- Majorana FRG (PMFRG).
In my PhD thesis, PMFRG has been generalized and applied to highly frustrated spin systems. In particular, spin representations in terms of Majorana operators for spins with arbitrary large spin magnitude S are being investigated and classified thoroughly, which closes a gap in the literature about the second quantization of spin operators. Moreover, it is presented how to generalize PMFRG to models with only a U(1) symmetry, instead of the full SU(2) symmetry of the Heisenberg model that has been assumed previously in the literature. This opens up a wide range of interesting applications for PMFRG. In particular, we discuss the XXZ model on the pyrochlore lattice, where results are being compared to experiments and QMC simulations. Furthermore, the entire phase diagram of the XXZ model is being mapped out and the capability of PMFRG to reproduce low-energy field theory predictions and to determine critical exponents are being tested.
In my PhD thesis, PMFRG has been generalized and applied to highly frustrated spin systems. In particular, spin representations in terms of Majorana operators for spins with arbitrary large spin magnitude S are being investigated and classified thoroughly, which closes a gap in the literature about the second quantization of spin operators. Moreover, it is presented how to generalize PMFRG to models with only a U(1) symmetry, instead of the full SU(2) symmetry of the Heisenberg model that has been assumed previously in the literature. This opens up a wide range of interesting applications for PMFRG. In particular, we discuss the XXZ model on the pyrochlore lattice, where results are being compared to experiments and QMC simulations. Furthermore, the entire phase diagram of the XXZ model is being mapped out and the capability of PMFRG to reproduce low-energy field theory predictions and to determine critical exponents are being tested.
Time & Location
Nov 17, 2025 | 04:00 PM
Hörsaal A (1.3.14)
(Fachbereich Physik, Arnimallee 14, 14195 Berlin)