Entanglement of Low-Energy Excitations in Conformal Field Theory

Alcaraz, Francisco C.; Ibáñez-Berganza, Miguel; Sierra, Germȧn

doi:10.1103/physrevlett.106.201601

Cited by 188 publications

(342 citation statements)

References 23 publications

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“…In Ref. [46] it has been shown that the entanglement entropies of low-lying excited states display a universal finite size scaling that is different from the one in the ground state of Eq. (3).…”

Section: Excited States In Periodic Chainsmentioning

confidence: 99%

The entanglement entropy of one-dimensional systems in continuous and homogeneous space

Calabrese¹,

Mintchev²,

Vicari³

2011

J. Stat. Mech.

128

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Abstract.We introduce a systematic framework to calculate the bipartite entanglement entropy of a compact spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. We show that when working with a finite number of particles N , the Rényi entanglement entropies grow as ln N , with a prefactor that is given by the central charge. We apply this novel technique to the ground state and to excited states of periodic systems. We also consider systems with boundaries. We derive universal formulas for the leading behavior and for subleading corrections to the scaling. The universality of the results allows us to make predictions for the finite-size scaling forms of the corrections to the scaling.arXiv:1107.3985v2 [cond-mat.stat-mech]

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Section: Excited States In Periodic Chainsmentioning

confidence: 99%

The entanglement entropy of one-dimensional systems in continuous and homogeneous space

Calabrese¹,

Mintchev²,

Vicari³

2011

J. Stat. Mech.

128

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“…[5,6] for some results in various CFT setups and Ref. [7] for entanglement in a related class of globally excited states. In 2d CFT this analysis can be preformed analytically and Rényi entropies detect an increase in entanglement equal to the logarithm of the quantum dimension of the conformal family [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Quantum dimensions from local operator excitations in the Ising model

Caputa

Rams

2017

J. Phys. A: Math. Theor.

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We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Rényi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as the evolution of the relative entropy after local operator excitation and discuss universal features that emerge from numerics.

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“…In 2D rational CFTs, it was found [15] that for the locally primary excited states, the Rényi entropy difference is related to the quantum dimension [5][6][7][8][9] of the primary operator, which is a kind of topological quantity. The computations of the entanglement entropies for locally excited states have been formulated in [10][11][12] in the field theory side. The entanglement entropy for local free scalar have…”

Section: Introductionmentioning

confidence: 99%

Entanglement entropy for descendent local operators in 2D CFTs

Chen

Guo

et al. 2015

J. High Energ. Phys.

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We mainly study the Rényi entropy and entanglement entropy of the states locally excited by the descendent operators in two dimensional conformal field theories (CFTs). In rational CFTs, we prove that the increase of entanglement entropy and Rényi entropy for a class of descendent operators, which are generated by L (−)L(−) onto the primary operator, always coincide with the logarithmic of quantum dimension of the corresponding primary operator. That means the Rényi entropy and entanglement entropy for these descendent operators are the same as the ones of their corresponding primary operator. For 2D rational CFTs with a boundary, we confirm that the Rényi entropy always coincides with the logarithmic of quantum dimension of the primary operator during some periods of the evolution. Furthermore, we consider more general descendent operators generated by d {n i }{n j } ( i L −n i jL −n j ) on the primary operator. For these operators, the entanglement entropy and Rényi entropy get additional corrections, as the mixing of holomorphic and anti-holomorphic Virasoro generators enhance the entanglement. Finally, we employ perturbative CFT techniques to evaluate the Rényi entropy of the excited operators in deformed CFT. The Rényi and entanglement entropies are increased, and get contributions not only from local excited operators but also from global deformation of the theory.

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Entanglement of Low-Energy Excitations in Conformal Field Theory

Cited by 188 publications

References 23 publications

The entanglement entropy of one-dimensional systems in continuous and homogeneous space

The entanglement entropy of one-dimensional systems in continuous and homogeneous space

Quantum dimensions from local operator excitations in the Ising model

Entanglement entropy for descendent local operators in 2D CFTs

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