Bulk-boundary correspondence in the quantum Hall effect

Cappelli, Andrea; Maffi, Lorenzo

doi:10.1088/1751-8121/aad0ab

Cited by 13 publications

(24 citation statements)

References 53 publications

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“…This quantity matches (3.15) upon using the expression of wavefunctions (2.8) in the limit to the edge [29],…”

Section: Radial Shape Of Neutral Excitationssupporting

confidence: 69%

“…As formulated in ref. [29], this amounts to the combined expansion of radii r and angular momenta m for values near the edge of the droplet, as follows:…”

Section: Jhep05(2021)120mentioning

confidence: 99%

“…A first understanding of the bulk-boundary map was obtained only recently, by a more careful definition of the edge limit [29] (see also [48]). It was shown that the modes of the and by taking the limit R → ∞ for values of coordinate r and angular momentum m at the edge of the droplet, as follows:…”

Section: Laplace Transform and Bulk-boundary Mapmentioning

confidence: 99%

“…In this limit, the ρ n become operators in the edge conformal theory and obey the expected current algebra commutation relations, [ρ n , ρ m ] = nδ n+m,0 [29].…”

Section: Laplace Transform and Bulk-boundary Mapmentioning

confidence: 99%

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W-infinity symmetry in the quantum hall effect beyond the edge

Cappelli

Maffi

2021

J. High Energ. Phys.

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The description of chiral quantum incompressible fluids by the W∞ symmetry can be extended from the edge, where it encompasses the conformal field theory approach, to the non-conformal bulk. The two regimes are characterized by excitations with different sizes, energies and momenta within the disk geometry. In particular, the bulk quantities have a finite limit for large droplets. We obtain analytic results for the radial shape of excitations, the edge reconstruction phenomenon and the energy spectrum of density fluctuations in Laughlin states.

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“…This quantity matches (3.15) upon using the expression of wavefunctions (2.8) in the limit to the edge [29],…”

Section: Radial Shape Of Neutral Excitationssupporting

confidence: 69%

“…As formulated in ref. [29], this amounts to the combined expansion of radii r and angular momenta m for values near the edge of the droplet, as follows:…”

Section: Jhep05(2021)120mentioning

confidence: 99%

Section: Laplace Transform and Bulk-boundary Mapmentioning

confidence: 99%

“…In this limit, the ρ n become operators in the edge conformal theory and obey the expected current algebra commutation relations, [ρ n , ρ m ] = nδ n+m,0 [29].…”

Section: Laplace Transform and Bulk-boundary Mapmentioning

confidence: 99%

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W-infinity symmetry in the quantum hall effect beyond the edge

Cappelli

Maffi

2021

J. High Energ. Phys.

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“…One of the most outstanding issues of entanglement features is that entanglement entropy is somehow bounded by the area of quantum systems. This idea, now as an important part of holography principle, can be applied into many different physical areas, such as topological order [1][2][3], fractional quantum hall effect [4], topological insulator and topological superconductor [5,6], anti-de Sitter space/conformal field theory (AdS/CFT) correspondence [7-10] and so on.…”

Section: Introductionmentioning

confidence: 99%

Entanglement area law for shallow and deep quantum neural network states

Jia

et al. 2020

New J. Phys.

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A study of the artificial neural network representation of quantum many-body states is presented. The locality and entanglement properties of states for shallow and deep quantum neural networks are investigated in detail. By introducing the notion of local quasi-product states, for which the locally connected shallow feed-forward neural network states and restricted Boltzmann machine states are special cases, we show that Rényi entanglement entropies of all these states obey the entanglement area law. Besides, we also investigate the entanglement features of deep Boltzmann machine states and show that locality constraints imposed on the neural networks make the states obey the entanglement area law. Finally, as an application, we apply the notion of Rényi entanglement entropy to understand the power of neural networks, and show that image classification problems can be efficiently solved must obey the area law.

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Boundary central charge from bulk odd viscosity: Chiral superfluids

2019

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We derive a low energy effective field theory for chiral superfluids, which accounts for both spontaneous symmetry breaking and fermionic ground-state topology. Using the theory, we show that the odd (or Hall) viscosity tensor, at small wave-vector, contains a dependence on the chiral central charge c of the boundary degrees of freedom, as well as additional non-universal contributions. We identify related bulk observables which allow for a bulk measurement of c. In Galilean invariant superfluids, only the particle current and density responses to strain and electromagnetic fields are required. To complement our results, the effective theory is benchmarked against a perturbative computation within a canonical microscopic model. < l a t e x i t s h a 1 _ b a s e 6 4 = " r L w / X U c T o a 2 Z e K G I 9 H 4 s i a p 2 4 C g = " > A A A B 6 n i c b V B N S w M x E J 2 t X 7 V + V T 1 6 C R b B U 9 k V Q b 0 V v X i s 4 N p C u 5 R s m m 1 D k 2 x I s k J Z + h e 8 e F D x 6 i / y 5 r 8 x 2 + 5 B q w 8 G H u / N M D M v V p w Z 6 / t f X m V l d W 1 9 o 7 p Z 2 9 r e 2 d 2 r 7 x 8 8 m D T T h I Y k 5 a n u x t h Q z i Q N L b O c d p W m W M S c d u L J T e F 3 H q k 2 L J X 3 d q p o J P B I s o Q R b A u p r w w b 1 B t + 0 5 8 D / S V B S R p Q o j 2 o f / a H K c k E l Z Z w b E w v 8 J W N c q w t I 5 z O a v 3 M U I X J B I 9 o z 1 G J B T V R P r 9 1 h k 6 c M k R J q l 1 J i + b q z 4 k c C 2 O m I n a d A t u x W f Y K 8 T + v l 9 n k M s q Z V J m l k i S w M x E J 2 t X 7 V + V T 1 6 C R b B U 9 k V Q b 0 V v X i s 4 N p C u 5 R s m m 1 D k 2 x I s k J Z + h e 8 e F D x 6 i / y 5 r 8 x 2 + 5 B q w 8 G H u / N M D M v V p w Z 6 / t f X m V l d W 1 9 o 7 p Z 2 9 r e 2 d 2 r 7 x 8 8 m D T T h I Y k 5 a n u x t h Q z i Q N L b O c d p W m W M S c d u L J T e F 3 H q k 2 L J X 3 d q p o J P B I s o Q R b A u p r w w b 1 B t + 0 5 8 D / S V B S R p Q o j 2 o f / a H K c k E l Z Z w b E w v 8 J W N c q w t I 5 z O a v 3 M U I X J B I 9 o z 1 G J B T V R P r 9 1 h k 6 c M k R J q l 1 J i + b q z 4 k c C 2 O m I n a d A t u x W f Y K 8 T + v l 9 n k M s q Z V J m l k i S w M x E J 2 t X 7 V + V T 1 6 C R b B U 9 k V Q b 0 V v X i s 4 N p C u 5 R s m m 1 D k 2 x I s k J Z + h e 8 e F D x 6 i / y 5 r 8 x 2 + 5 B q w 8 G H u / N M D M v V p w Z 6 / t f X m V l d W 1 9 o 7 p Z 2 9 r e 2 d 2 r 7 x 8 8 m D T T h I Y k 5 a n u x t h Q z i Q N L b O c d p W m W M S c d u L J T e F 3 H q k 2 L J X 3 d q p o J P B I s o Q R b A u p r w w b 1 B t + 0 5 8 D / S V B S R p Q o j 2 o f / a H K c k E l Z Z w b E w v 8 J W N c q w t I 5 z O a v 3 M U I X J B I 9 o z 1 G J B T V R P r 9 1 h k 6 c M k R J q l 1 J i + b q z 4 k c C 2 O m I n a d A t u x W f Y K 8 T + v l 9 n k M s q Z V J m l k i S w M x E J 2 t X 7 V + V T 1 6 C R b B U 9 k V Q b 0 V v X i s 4 N p C u 5 R s m m 1 D k 2 x I s k J Z + h e 8 e F D x 6 i / y 5 r 8 x 2 + 5 B q w 8 G H u / N M D M v V p w Z 6 / t f X m V l d W 1 9 o 7 p Z 2 9 r e 2 d 2 r 7 x 8 8 m D T T h I Y k 5 a n u x t h Q z i Q N L b O c d p W m W M S c d u L J T e F 3 H q k 2 L J X 3 d q p o J P B I ...

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Bulk-boundary correspondence in the quantum Hall effect

Cited by 13 publications

References 53 publications

W-infinity symmetry in the quantum hall effect beyond the edge

W-infinity symmetry in the quantum hall effect beyond the edge

Entanglement area law for shallow and deep quantum neural network states

Boundary central charge from bulk odd viscosity: Chiral superfluids

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