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 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 Interacting Floquet topological phases in three dimensions

2018 ◽  
Vol 98 (4) ◽  
Author(s):  
Dominic Reiss ◽  
Fenner Harper ◽  
Rahul Roy
Keyword(s):  
Three Dimensions ◽  
Topological Phases

scholarly journals On the Exact Variance of Tsallis Entanglement Entropy in a Random Pure State

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 539 ◽  
Author(s):  
Lu Wei
Keyword(s):  
Pure State ◽  
Entanglement Entropy ◽  
Tsallis Entropy ◽  
Von Neumann Entropy ◽  
Quadratic Entropy ◽  
Von Neumann ◽  
Special Cases ◽  
Variance Formula ◽  
Finite Sums ◽  
Random Pure State

The Tsallis entropy is a useful one-parameter generalization to the standard von Neumann entropy in quantum information theory. In this work, we study the variance of the Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact variance formula of the Tsallis entropy that involves finite sums of some terminating hypergeometric functions. In the special cases of quadratic entropy and small subsystem dimensions, the main result is further simplified to explicit variance expressions. As a byproduct, we find an independent proof of the recently proven variance formula of the von Neumann entropy based on the derived moment relation to the Tsallis entropy.

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 A field theory study of entanglement wedge cross section: odd entropy

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Ali Mollabashi ◽  
Kotaro Tamaoka
Keyword(s):  
Cross Section ◽  
Entanglement Entropy ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Mixed States ◽  
Scale Invariant ◽  
Gaussian States ◽  
Von Neumann ◽  
Free Scalar ◽  
The Difference

Abstract We study odd entanglement entropy (odd entropy in short), a candidate of measure for mixed states holographically dual to the entanglement wedge cross section, in two-dimensional free scalar field theories. Our study is restricted to Gaussian states of scale-invariant theories as well as their finite temperature generalizations, for which we show that odd entropy is a well-defined measure for mixed states. Motivated from holographic results, the difference between odd and von Neumann entropy is also studied. In particular, we show that large amounts of quantum correlations ensure the odd entropy to be larger than von Neumann entropy, which is qualitatively consistent with the holographic CFT. In general cases, we also find that this difference is not even a monotonic function with respect to size of (and distance between) subsystems.

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