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TT: Fachverband Tiefe Temperaturen

TT 23: Correlated Electrons – Poster I

TT 23.6: Poster

Montag, 9. März 2026, 18:00–20:00, P1

The XY Toric Code on the Kagome lattice — •Constanze Kölbl, Maximilian Vieweg, and Kai Phillip Schmidt — Department Physik, Staudtstraße 7, 91058 Erlangen

This theoretical work investigates the XY toric tode on the Kagome lattice, constituting a generalisation of the 2024 introduced XY checkerboard toric code on the square lattice [1]. Main objectives are deriving ground state and low-excitation properties and further extracting the parameter-dependent quantum phase diagram of the model. Besides a four-spin z-flavour star operator, two kinds of plaquette operators are introduced, including both Pauli x and y interactions and realising a bipartition. Due to the geometry of the lattice, the plaquette operators connect three and six spins each. Star operators still act as symmetries of the Hamiltonian, whereas different plaquette operator types generally do not commute. The behaviour in the limit of isolated plaquettes is examined analytically using first-order perturbation theory, checking for topological order. Further intuition is gained from exact diagonalisation of the full Hamiltonian for a system comprising 24 spins. A duality mapping is performed, giving rise to a self-dual model built from four- and six-spin Ising interactions. Symmetries of the dual model are investigated, and high-order perturbation theory is performed. The general goal is to understand the influence of geometry on the physical properties of topological codes.
[1] M. Vieweg, K.P. Schmidt, Phys. Rev. Res., 7 (2025)

Keywords: Toric Code; Kagomé lattice; Topological Order