scholarly journals Topological entanglement entropy of the three-dimensional Kitaev model

2018 ◽  
Vol 98 (12) ◽  
Author(s):  
N. C. Randeep ◽  
Naveen Surendran
Keyword(s):  
Entanglement Entropy ◽  
Three Dimensional ◽  
Kitaev Model ◽  
Topological Entanglement Entropy

scholarly journals Topological pseudo entropy

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Tatsuma Nishioka ◽  
Tadashi Takayanagi ◽  
Yusuke Taki
Keyword(s):  
Entanglement Entropy ◽  
Three Dimensional ◽  
Partition Functions ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Conformal Field ◽  
Boundary States ◽  
Dimensional Boundary ◽  
Topological Entanglement Entropy ◽  
Chern Simons

Abstract We introduce a pseudo entropy extension of topological entanglement entropy called topological pseudo entropy. Various examples of the topological pseudo entropies are examined in three-dimensional Chern-Simons gauge theory with Wilson loop insertions. Partition functions with knotted Wilson loops are directly related to topological pseudo (Rényi) entropies. We also show that the pseudo entropy in a certain setup is equivalent to the interface entropy in two-dimensional conformal field theories (CFTs), and leverage the equivalence to calculate the pseudo entropies in particular examples. Furthermore, we define a pseudo entropy extension of the left-right entanglement entropy in two-dimensional boundary CFTs and derive a universal formula for a pair of arbitrary boundary states. As a byproduct, we find that the topological interface entropy for rational CFTs has a contribution identical to the topological entanglement entropy on a torus.

scholarly journals Universal entanglement signatures of foliated fracton phases

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Wilbur Shirley ◽  
Kevin Slagle ◽  
Xie Chen
Keyword(s):  
Fixed Point ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Topological Phases ◽  
Topological Order ◽  
Two Dimensional ◽  
Adiabatic Evolution ◽  
Universal Properties ◽  
Three Dimensional Models ◽  
Topological Entanglement Entropy

Fracton models exhibit a variety of exotic properties and lie beyond the conventional framework of gapped topological order. In , we generalized the notion of gapped phase to one of foliated fracton phase by allowing the addition of layers of gapped two-dimensional resources in the adiabatic evolution between gapped three-dimensional models. Moreover, we showed that the X-cube model is a fixed point of one such phase. In this paper, according to this definition, we look for universal properties of such phases which remain invariant throughout the entire phase. We propose multi-partite entanglement quantities, generalizing the proposal of topological entanglement entropy designed for conventional topological phases. We present arguments for the universality of these quantities and show that they attain non-zero constant value in non-trivial foliated fracton phases.

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 Topological Entanglement Entropy with a Twist

2013 ◽  
Vol 111 (22) ◽  
Author(s):  
Benjamin J. Brown ◽  
Stephen D. Bartlett ◽  
Andrew C. Doherty ◽  
Sean D. Barrett
Keyword(s):  
Entanglement Entropy ◽  
Topological Entanglement Entropy

scholarly journals Topological entanglement entropy in Gutzwiller projected spin liquids

2013 ◽  
Vol 88 (12) ◽  
Author(s):  
Jiquan Pei ◽  
Steve Han ◽  
Haijun Liao ◽  
Tao Li
Keyword(s):  
Entanglement Entropy ◽  
Spin Liquids ◽  
Topological Entanglement Entropy

scholarly journals Topological entanglement entropy and holography

2008 ◽  
Vol 2008 (07) ◽  
pp. 097-097 ◽  
Author(s):  
Ari Pakman ◽  
Andrei Parnachev
Keyword(s):  
Entanglement Entropy ◽  
Topological Entanglement Entropy
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