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

2021/06/30 by Matthias Mühlhauser, M. Mühlhauser, K. P. Schmidt +5 · 16 citations
Mathematics · Physics and Astronomy · #Combinatorics #Hamiltonian (control theory) #Limiting #Mathematics #Phase (matter) #Phase diagram #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Theoretical physics #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #Toric code #cond-mat.str-el

paper · pdf · open access · doi:10.21468/scipostphys.12.2.069

published in SciPost Physics 12(2) (SciPost.org) · 14 pages, 5 figures

openalex publication_date 2022/02/22 · openalex created_date 2022/02/24 · arxiv created 2022/03/18 · arxiv updated 2022/03/21 · openalex updated_date 2026/08/05

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.

Citations

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