We consider the logarithmic negativity of a finite interval embedded in an infinite one dimensional system at finite temperature. We focus on conformal invariant systems and we show that the naive approach based on the calculation of a two-point function of twist fields in a cylindrical geometry yields a wrong result. The correct result is obtained through a four-point function of twist fields in which two auxiliary fields are inserted far away from the interval, and they are sent to infinity only after having taken the replica limit. In this way, we find a universal scaling form for the finite temperature negativity which depends on the full operator content of the theory and not only on the central charge. In the limit of low and high temperatures, the expansion of this universal form can be obtained by means of the operator product expansion. We check our results against exact numerical computations for the critical harmonic chain.

Finite temperature entanglement negativity in conformal field theory / Calabrese, Pasquale; Cardy, J; Tonni, Erik. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 48:1(2015), pp. 1-23. [10.1088/1751-8113/48/1/015006]

Finite temperature entanglement negativity in conformal field theory

Calabrese, Pasquale;Tonni, Erik
2015-01-01

Abstract

We consider the logarithmic negativity of a finite interval embedded in an infinite one dimensional system at finite temperature. We focus on conformal invariant systems and we show that the naive approach based on the calculation of a two-point function of twist fields in a cylindrical geometry yields a wrong result. The correct result is obtained through a four-point function of twist fields in which two auxiliary fields are inserted far away from the interval, and they are sent to infinity only after having taken the replica limit. In this way, we find a universal scaling form for the finite temperature negativity which depends on the full operator content of the theory and not only on the central charge. In the limit of low and high temperatures, the expansion of this universal form can be obtained by means of the operator product expansion. We check our results against exact numerical computations for the critical harmonic chain.
2015
48
1
1
23
015006
https://doi.org/10.1088/1751-8113/48/1/015006
http://iopscience.iop.org/article/10.1088/1751-8113/48/1/015006
https://arxiv.org/abs/1408.3043
Calabrese, Pasquale; Cardy, J; Tonni, Erik
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11548
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