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arXiv · 1612.00659

Relative Entanglement Entropies in 1+1-dimensional conformal field theories

Paola Ruggiero·Pasquale Calabrese
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Abstract

We study the relative entanglement entropies of one interval between excited states of a 1+1 dimensional conformal field theory (CFT). To compute the relative entropy $S(ρ_1 \| ρ_0)$ between two given reduced density matrices $ρ_1$ and $ρ_0$ of a quantum field theory, we employ the replica trick which relies on the path integral representation of ${\rm Tr} ( ρ_1 ρ_0^{n-1} )$ and define a set of Rényi relative entropies $S_n(ρ_1 \| ρ_0)$. We compute these quantities for integer values of the parameter $n$ and derive via the replica limit, the relative entropy between excited states generated by primary fields of a free massless bosonic field. In particular, we provide the relative entanglement entropy of the state described by the primary operator $i \partialϕ$, both with respect to the ground state and to the state generated by chiral vertex operators. These predictions are tested against exact numerical calculations in the XX spin-chain finding perfect agreement.

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Paola Ruggiero, Pasquale Calabrese. 2016-12-12. Relative Entanglement Entropies in 1+1-dimensional conformal field theories. https://doi.org/10.1007/jhep02(2017)039

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