Entanglement entropy in the Long-Range Kitaev chain

TL;DR

This paper investigates how long-range pairing interactions in the Kitaev chain affect entanglement entropy, revealing non-universal growth and loss of conformal symmetry at critical decay exponents.

Contribution

It introduces a new analytical technique for asymptotic analysis of block Toeplitz determinants with discontinuities and explores the entropy behavior in long-range Kitaev chains.

Findings

Entanglement entropy growth becomes non-universal at critical decay exponents.

Loss of conformal field theory connection in the asymptotic behavior.

Development of a new method for analyzing block Toeplitz determinants.

Abstract

In this paper we complete the study on the asymptotic behaviour of the entanglement entropy for Kitaev chains with long range pairing. We discover that when the couplings decay with the distance with a critical exponent new properties for the asymptotic growth of the entropy appear. The coefficient of the leading term is not universal any more and the connection with conformal field theories is lost. We perform a numerical and analytical approach to the problem showing a perfect agreement. In order to carry out the analytical study, a new technique for computing the asymptotic behaviour of block Toeplitz determinants with discontinuous symbols has been developed.