Quantum dimension as entanglement entropy in two dimensional conformal field theories

He, Song; Numasawa, Tokiro; Takayanagi, Tadashi; Watanabe, Kento

doi:10.1103/physrevd.90.041701

Cited by 128 publications

(281 citation statements)

References 16 publications

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“…In particular, for different methods of local quenches [21,22,[28][29][30], the shape of entangled pairs may be very different. A quantitative study of this question as well as its application to the finite temperature case will be reported elsewhere [40].…”

Section: Comparison Between Cft Results and Numerical Resultsmentioning

confidence: 99%

“…In our work, a local quantum quench is realized by joining two separate CFTs at the endpoints. Another method to realize a local quantum quench is through acting with a local operator on an infinitely extended system [28][29][30]. By studying the increase of the Renyi entropy at a later time, quantum entanglement of local operators can be detected.…”

Section: B Conclusionmentioning

confidence: 99%

“…pairs [28][29][30][31][32] which carry entanglement information. When the entangled pairs arrive at two intervals separately, the entanglement negativity can be built immediately.…”

Section: Introduction a Introductionmentioning

confidence: 99%

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Entanglement negativity after a local quantum quench in conformal field theories

2015

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We study the time evolution of the entanglement negativity after a local quantum quench in (1+1)-dimensional conformal field theories (CFTs), which we introduce by suddenly joining two initially decoupled CFTs at their endpoints. We calculate the negativity evolution for both adjacent intervals and disjoint intervals explicitly. For two adjacent intervals, the entanglement negativity grows logarithmically in time right after the quench. After developing a plateau-like feature, the entanglement negativity drops to the ground-state value. For the case of two spatially separated intervals, a light-cone behavior is observed in the negativity evolution; in addition, a long-range entanglement, which is independent of the distance between two intervals, can be created. Our results agree with the heuristic picture that quasiparticles, which carry entanglement, are emitted from the joining point and propagate freely through the system. Our analytical results are confirmed by numerical calculations based on a critical harmonic chain.

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Section: Comparison Between Cft Results and Numerical Resultsmentioning

confidence: 99%

Section: B Conclusionmentioning

confidence: 99%

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Entanglement negativity after a local quantum quench in conformal field theories

2015

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“…There have also been some recent work discussing excited states in CFT's in various dimensions [11][12][13][14].…”

Section: Jhep01(2015)110mentioning

confidence: 99%

Left-right entanglement entropy of boundary states

Zayas

Quiroz

2015

J. High Energ. Phys.

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Abstract:We study entanglement entropy of boundary states in a free bosonic conformal field theory. A boundary state can be thought of as composed of a particular combination of left and right-moving modes of the two-dimensional conformal field theory. We investigate the reduced density matrix obtained by tracing over the right-moving modes in various boundary states. We consider Dirichlet and Neumann boundary states of a free noncompact as well as a compact boson. The results for the entanglement entropy indicate that the reduced system can be viewed as a thermal CFT gas. Our findings are in agreement and generalize results in quantum mechanics and quantum field theory where coherent states can also be considered. In the compact case we verify that the entanglement entropy expressions are consistent with T-duality.

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“…Also we would like to refer to [74] for large N CFTs and refer to [72] for rational CFTs in two dimensions.…”

Section: Jhep10(2014)147mentioning

confidence: 99%

Notes on quantum entanglement of local operators

Nozaki

2014

J. High Energ. Phys.

140

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This is an expanded version of the short report arXiv:1401.0539, where we studied the time evolution of (Renyi) entanglement entropies for the excited state defined by acting a given local operator on the ground state. In the present paper, we introduce (Renyi) entanglement entropies of given local operators which are defined by late time values of excesses of (Renyi) entanglement entropies. They measure the degrees of freedom of local operators and characterize them in conformal field theories from the viewpoint of quantum entanglement. We explain how to compute them in free massless scalar field theories and we also investigate their time evolution. Our results can be interpreted in terms of the relativistic propagation of entangled pairs. The main new results which we acquire in the present paper are as follows. Firstly, we provide an explanation which shows that (Renyi) entanglement entropies of a specific operator are given by (Renyi) entanglement entropies whose reduced density matrices are given by the binomial distribution. That operator is constructed of only the scalar field. Secondly, we found the sum rule which (Renyi) entanglement entropies of those local operators obey. Those local operators are located separately. Moreover we argue that (Renyi) entanglement entropies of specific operators in conformal field theories are given by (Renyi) entanglement entropies whose reduced density matrices are given by the binomial distribution. These specific operators are constructed of single-species operators. We also argue that general operators obey the sum rule which we mentioned above.

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Quantum dimension as entanglement entropy in two dimensional conformal field theories

Cited by 128 publications

References 16 publications

Entanglement negativity after a local quantum quench in conformal field theories

Entanglement negativity after a local quantum quench in conformal field theories

Left-right entanglement entropy of boundary states

Notes on quantum entanglement of local operators

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