Dresden 2026 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 23: Correlated Electrons – Poster I

TT 23.5: Poster

Monday, March 9, 2026, 18:00–20:00, P1

Quantum Phase Transitions of Kitaev's Toric Code on a Honeycomb lattice — •Viktor Kott, Matthias Mühlhauser, Jan Alexander Koziol, and Kai Phillip Schmidt — Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)

We investigate the robustness of the topological phase of Kitaev's toric code in a uniform magnetic field on the honeycomb (and triangular) lattice using perturbative linked-cluster expansions (LCEs) based on a hypergraph decomposition, together with quantum Monte Carlo (QMC) simulations. The LCE approach allows us to correctly account for the nontrivial mutual exchange statistics of elementary anyonic excitations. By extracting the ground-state energy and excitation energies of the topological phase, we determine the quantum phase transitions out of the topologically ordered state. In addition, we use QMC to explore the full quantum phase diagram. In contrast to the conventional toric code on the square lattice, the ground-state phase diagram depends on the sign of the magnetic field, which distinguishes between unfrustrated and frustrated parameter regimes. This leads to distinct quantum-critical properties and a richer phase diagram.

Keywords: Toric Code; Quantum monte carlo; Frustration; Topological order