### Abstract

We calculate the entanglement entropy of a non-contiguous subsystem of a chain of free fermions. The starting point is a formula suggested by Jin and Korepin, arXiv:1104.1004, for the reduced density of states of two disjoint intervals with lattice sites P={1,2,...,m}\cup{2m+1,2m+2,..., 3m}, which applies to this model. As a first step in the asymptotic analysis of this system, we consider its simplification to two disjoint intervals separated just by one site, and we rigorously calculate the mutual information between these two blocks and the rest of the chain. In order to compute the entropy we need to study the asymptotic behaviour of an inverse Toeplitz matrix with Fisher-Hartwig symbol using the the Riemann--Hilbert method.

Original language | English |
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Article number | 345303 |

Number of pages | 32 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 53 |

Issue number | 34 |

Early online date | 15 Jun 2020 |

DOIs | |

Publication status | Published - 3 Aug 2020 |

### Keywords

- quantum spin chain
- quantum entanglement entropy
- mutual information
- Riemann-Hilbert problems

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## Cite this

Brightmore, L., Gehér, G. P., Its, A. R., Korepin, V. E., Mezzadri, F., Mo, M. Y., & Virtanen, J. A. (2020). Entanglement entropy of two disjoint intervals separated by one spin in a chain of free fermions.

*Journal of Physics A: Mathematical and Theoretical*,*53*(34), [345303]. https://doi.org/10.1088/1751-8121/ab9cf2