We investigate the effect of a global degeneracy in the distribution of the entanglement spectrum in conformal field theories in one spatial dimension. We relate the recently found universal expression for the entanglement Hamiltonian to the distribution of the entanglement spectrum. The main tool to establish this connection is the Cardy formula. It turns out that the Affleck-Ludwig non-integer degeneracy, appearing because of the boundary conditions induced at the entangling surface, can be directly read from the entanglement spectrum distribution. We also clarify the effect of the noninteger degeneracy on the spectrum of the partial transpose, which is the central object for quantifying the entanglement in mixed states. We show that the exact knowledge of the entanglement spectrum in some integrable spinchains provides strong analytical evidences corroborating our results.

Entanglement spectrum degeneracy and the Cardy formula in 1+1 dimensional conformal field theories / Alba, Vincenzo; Calabrese, Pasquale; Tonni, Erik. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 51:2(2018), pp. 1-23. [10.1088/1751-8121/aa9365]

Entanglement spectrum degeneracy and the Cardy formula in 1+1 dimensional conformal field theories

Alba, Vincenzo
;
Calabrese, Pasquale;Tonni, Erik
2018

Abstract

We investigate the effect of a global degeneracy in the distribution of the entanglement spectrum in conformal field theories in one spatial dimension. We relate the recently found universal expression for the entanglement Hamiltonian to the distribution of the entanglement spectrum. The main tool to establish this connection is the Cardy formula. It turns out that the Affleck-Ludwig non-integer degeneracy, appearing because of the boundary conditions induced at the entangling surface, can be directly read from the entanglement spectrum distribution. We also clarify the effect of the noninteger degeneracy on the spectrum of the partial transpose, which is the central object for quantifying the entanglement in mixed states. We show that the exact knowledge of the entanglement spectrum in some integrable spinchains provides strong analytical evidences corroborating our results.
51
2
1
23
024001
10.1088/1751-8121/aa9365
https://doi.org/10.1088/1751-8121/aa9365
https://arxiv.org/abs/1707.07532
Alba, Vincenzo; Calabrese, Pasquale; Tonni, Erik
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/67590
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