scholarly journals Entanglement entropy of gapped phases and topological order in three dimensions

2011 ◽  
Vol 84 (19) ◽  
Author(s):  
Tarun Grover ◽  
Ari M. Turner ◽  
Ashvin Vishwanath
Keyword(s):  
Entanglement Entropy ◽  
Three Dimensions ◽  
Topological Order

scholarly journals Boundary Topological Entanglement Entropy in Two and Three Dimensions

2021 ◽  
Author(s):  
Jacob C. Bridgeman ◽  
Benjamin J. Brown ◽  
Samuel J. Elman
Keyword(s):  
General Property ◽  
Entanglement Entropy ◽  
Quantum Correlations ◽  
Three Dimensions ◽  
Topological Phases ◽  
Fusion Categories ◽  
Special Cases ◽  
Constructive Proofs ◽  
And Algebra ◽  
Topological Entanglement Entropy

AbstractThe topological entanglement entropy is used to measure long-range quantum correlations in the ground space of topological phases. Here we obtain closed form expressions for the topological entropy of (2+1)- and (3+1)-dimensional loop gas models, both in the bulk and at their boundaries, in terms of the data of their input fusion categories and algebra objects. Central to the formulation of our results are generalized $${\mathcal {S}}$$ S -matrices. We conjecture a general property of these $${\mathcal {S}}$$ S -matrices, with proofs provided in many special cases. This includes constructive proofs for categories up to rank 5.

scholarly journals Detecting subsystem symmetry protected topological order via entanglement entropy

2019 ◽  
Vol 100 (11) ◽  
Author(s):  
David T. Stephen ◽  
Henrik Dreyer ◽  
Mohsin Iqbal ◽  
Norbert Schuch
Keyword(s):  
Entanglement Entropy ◽  
Topological Order ◽  
Symmetry Protected

scholarly journals Entanglement entropy for (3+1)-dimensional topological order with excitations

2018 ◽  
Vol 97 (8) ◽  
Author(s):  
Xueda Wen ◽  
Huan He ◽  
Apoorv Tiwari ◽  
Yunqin Zheng ◽  
Peng Ye
Keyword(s):  
Entanglement Entropy ◽  
Topological Order

scholarly journals Local disorder, topological ground state degeneracy and entanglement entropy, and discrete anyons

2017 ◽  
Vol 29 (06) ◽  
pp. 1750018 ◽  
Author(s):  
Sven Bachmann
Keyword(s):  
Ground State ◽  
Entanglement Entropy ◽  
Orientable Surface ◽  
Cell Complex ◽  
Local Order ◽  
Topological Order ◽  
Cohomology Groups ◽  
Closed Orientable Surface ◽  
Ground State Degeneracy ◽  
Comprehensive Study

In this comprehensive study of Kitaev’s abelian models defined on a graph embedded on a closed orientable surface, we provide complete proofs of the topological ground state degeneracy, the absence of local order parameters, compute the entanglement entropy exactly and characterize the elementary anyonic excitations. The homology and cohomology groups of the cell complex play a central role and allow for a rigorous understanding of the relations between the above characterizations of topological order.

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