Entanglement entropy of two disjoint intervals separated by one spin in a chain of free fermion

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, \texttt{arXiv:1104.1004}, for the reduced density of states of two disjoint intervals with lattice sites $P=\{1,2,\dots ,m\}\cup \{2m+1,2m+2,\dots ,3m\}$, 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.

arXiv comment25 pages, 6 figures, title changed

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Cited by in corpus (6)

• Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains
• Long-range entanglement and topological excitations
• Mutual information for fermionic systems
• Exploring superconformal Yang-Mills theories through matrix Bessel kernels
• Asymptotics of block Toeplitz determinants with piecewise continuous symbols
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density