Competing topological orders in three dimensions: X-cube versus toric code

Abstract

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 displays 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.

14 pages, 5 figures

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Cited by in corpus (10)

• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Topological fracton quantum phase transitions by tuning exact tensor network states
• Projective cluster-additive transformation for quantum lattice models
• Linked Cluster Expansions via Hypergraph Decompositions
• Single-Shot Quantum Error Correction in Intertwined Toric Codes
• Series expansions in closed and open quantum many-body systems with multiple quasiparticle types
• Quantum phase transitions in the $K$-layer Ising toric code
• Foliated order parameter in a fracton phase transition
• ${\mathbb{Z}}_N$ generalizations of three-dimensional stabilizer codes
• Hidden subsystem symmetry protected states in competing topological orders