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 Entanglement signatures of emergent Dirac fermions: Kagome spin liquid and quantum criticality

2018 ◽  
Vol 4 (11) ◽  
pp. eaat5535 ◽  
Author(s):  
Wei Zhu ◽  
Xiao Chen ◽  
Yin-Chen He ◽  
William Witczak-Krempa
Keyword(s):  
Entanglement Entropy ◽  
Quantum Critical Point ◽  
Quantum Spin ◽  
Spin Liquid ◽  
Dirac Fermions ◽  
Spin Liquids ◽  
Density Matrix Renormalization ◽  
Dirac Semimetal ◽  
A Charge ◽  
Aharonov Bohm

Quantum spin liquids (QSLs) are exotic phases of matter that host fractionalized excitations. It is difficult for local probes to characterize QSL, whereas quantum entanglement can serve as a powerful diagnostic tool due to its nonlocality. The kagome antiferromagnetic Heisenberg model is one of the most studied and experimentally relevant models for QSL, but its solution remains under debate. Here, we perform a numerical Aharonov-Bohm experiment on this model and uncover universal features of the entanglement entropy. By means of the density matrix renormalization group, we reveal the entanglement signatures of emergent Dirac spinons, which are the fractionalized excitations of the QSL. This scheme provides qualitative insights into the nature of kagome QSL and can be used to study other quantum states of matter. As a concrete example, we also benchmark our methods on an interacting quantum critical point between a Dirac semimetal and a charge-ordered phase.

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 and holography

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

scholarly journals Topological Entanglement Entropy of Black Hole Interiors

2020 ◽  
pp. 1940001
Author(s):  
Eric Howard
Keyword(s):  
Black Hole ◽  
Long Range ◽  
Entanglement Entropy ◽  
Quantum Hall ◽  
Black Hole Entropy ◽  
Topological Quantum ◽  
Boundary Correspondence ◽  
Entropy Of Black Hole ◽  
Topological Entanglement Entropy ◽  
Chern Simons

Recent theoretical progress shows that ([Formula: see text]) black hole solution manifests long-range topological quantum entanglement similar to exotic non-Abelian excitations with fractional quantum statistics. In topologically ordered systems, there is a deep connection between physics of the bulk and that at the boundaries. Boundary terms play an important role in explaining the black hole entropy in general. We find several common properties between BTZ black holes and the Quantum Hall effect in ([Formula: see text])-dimensional bulk/boundary theories. We calculate the topological entanglement entropy of a ([Formula: see text]) black hole and recover the Bekenstein–Hawking entropy, showing that black hole entropy and topological entanglement entropy are related. Using Chern–Simons and Liouville theories, we find that long-range entanglement describes the interior geometry of a black hole and identify it with the boundary entropy as the bond required by the connectivity of spacetime, gluing the short-range entanglement described by the area law. The IR bulk–UV boundary correspondence can be realized as a UV low-excitation theory on the bulk matching the IR long-range excitations on the boundary theory. Several aspects of the current findings are discussed.

Sign in / Sign up

Export Citation Format

Share Document