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TT: Fachverband Tiefe Temperaturen

TT 80: Correlated Electrons: Poster

TT 80.20: Poster

Donnerstag, 21. März 2024, 15:00–18:00, Poster E

Quantum Phase Transitions of Kitaev's Toric Code on a Honeycomb lattice — •Viktor Kott, Matthias Mühlhauser, and Kai Phillip Schmidt — FAU, Erlangen-Nürnberg, Deutschland

We investigate the robustness of the topological phase of Kitaev's toric code in a uniform magnetic field on the honeycomb lattice through perturbative linked cluster expansions using a hypergraph decomposition. This approach allows us to correctly account for the non-trivial mutual exchange statistics of elementary anyonic excitations. By extracting the ground-state energy and excitation energies of the topological phase, we can determine the quantum phase transitions out of this topologically ordered state. In contrast to the conventional toric code on a square lattice, the ground-state phase diagram is dependent on the magnetic field's sign, which distinguishes between unfrustrated and frustrated parameter regimes. Consequently, this leads to distinct quantum-critical properties and a richer phase diagram.

Keywords: toric code; topological order; linked cluster expansions; hypergraph decomposition; magnetic perturbation