We study the competition between two different topological orders in three dimensions by considering the X-cube model and the three-dimensional toric code. The corresponding Hamiltonian can be decomposed into two commuting parts, one of which displaying a self-dual spectrum. To determine the phase diagram, we compute the high-order series expansions of the ground-state energy in all limiting cases. Apart from the topological order related to the toric code and the fractonic order related to the X-cube model, we found two new phases which are adiabatically connected to classical limits with nontrivial sub-extensive degeneracies. All phase transitions are found to be first order.
Cited by 9
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Friedrich-Alexander-Universität Erlangen-Nürnberg / University of Erlangen-Nuremberg [FAU]
- 2 Sorbonne Université / Sorbonne University