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Entanglement Content of Quantum Particle Excitations III. Graph Partition Functions

Castro-Alvaredo, O. ORCID: 0000-0003-1876-7341, Fazio, C. D., Doyon, B. and Szécsényi, I. M. (2019). Entanglement Content of Quantum Particle Excitations III. Graph Partition Functions. Journal of Mathematical Physics, 60, 082301.. doi: 10.1063/1.5098892

Abstract

We consider two measures of entanglement, the logarithmic negativity and the entanglement entropy, between regions of space in excited states of many-body systems formed by a finite number of particle excitations. In parts I and II of the current series of papers, it has been shown in one-dimensional free-particle models that, in the limit of large system's and regions' sizes, the contribution from the particles is given by the entanglement of natural qubit states, representing the uniform distribution of particles in space. We show that the replica logarithmic negativity and R\'enyi entanglement entropy of such qubit states are equal to the partition functions of certain graphs, that encode the connectivity of the manifold induced by permutation twist fields. Using this new connection to graph theory, we provide a general proof, in the massive free boson model, that the qubit result holds in any dimensionality, and for any regions' shapes and connectivity. The proof is based on clustering and the permutation-twist exchange relations, and is potentially generalisable to other situations, such as lattice models, particle and hole excitations above generalised Gibbs ensembles, and interacting integrable models.

Publication Type: Article
Additional Information: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared as Castro-Alvaredo, O. , Fazio, C. D., Doyon, B. and Szécsényi, I. M. (2019). Entanglement Content of Quantum Particle Excitations III. Graph Partition Functions. Journal of Mathematical Physics, 60, 082301. and may be found at https://doi.org/10.1063/1.5098892.
Publisher Keywords: Entanglement Entropy, Logarithmic Negativity, Excited States, Quantum Information, Graph Theory
Subjects: Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering
Date Deposited: 15 Aug 2019 15:51
URI: https://openaccess.city.ac.uk/id/eprint/22660
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