2021/04/30 by Pramod Padmanabhan, Fumihiko Sugino
Computer Science · Mathematics · Physics and Astronomy · #Anyon #Degenerate energy levels #Gauge theory #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Symmetry protected topological order #Theoretical physics #Topological degeneracy #Topological entropy in physics #Topological order #Topological quantum computer #Topological quantum number #Topology (electrical circuits) #Toric code #cond-mat.str-el #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1742-5468/ac25f7
published as J. Stat. Mech. (2021) 103103 · 51 pages, 14 figures, Published version. Includes a section on particle statistics on graphs and a fully worked out example
arxiv created 2021/09/22 · openalex publication_date 2021/10/01 · arxiv updated 2021/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of an even richer variety than the two-dimensional space. We explore this possibility by building a class of frustration-free and gapped Hamiltonians based on discrete abelian gauge groups. The resulting models have a ground state degeneracy that can be either a topological invariant, an extensive quantity or a mixture of the two. For two basis of the degenerate ground states which are complementary in quantum theory, the entanglement entropy (EE) is exactly computed. The result for one basis has a constant global term, known as the topological EE, implying long-range entanglement. On the other hand, the topological EE vanishes in the result for the other basis. Comparisons are made with similar occurrences in the toric code. We analyze excitations and identify anyon-like excitations that account for the topological EE. An analogy between the ground states of this system and the θ -vacuum for a U (1) gauge theory on a circle is also drawn.