Generalized Entanglement Entropy in New Spin Chains

We derive some entanglement properties of the ground states for two classes of quantum spin chains described by the Fredkin model, for half-integer spins, and the Motzkin model, for integer ones. Since the ground states of the two models are known analytically, we can calculate exactly the entanglement entropy, the negativity and the quantum mutual information. We show, in particular, that these systems exhibit long-distance entanglement, namely two disjoint regions of the chains remain entangled even when their separation is sent to infinity, i.e. these systems are not affected by decoherence. This strongly entangled behavior, Finally, we show that this behavior involves disjoint segments located both at the edges and in the bulk of the chains.

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Entanglement entropy of inhomogeneous XX spin chains with algebraic interactions

Journal of High Energy Physics ◽

10.1007/jhep12(2021)184 ◽

2021 ◽

Vol 2021 (12) ◽

Author(s):

Federico Finkel ◽

Artemio González-López

Keyword(s):

Magnetic Field ◽

Constant Magnetic Field ◽

Asymptotic Approximation ◽

Entanglement Entropy ◽

Inhomogeneous Magnetic Field ◽

Spin Chains ◽

Dirac Fermion ◽

Krawtchouk Polynomials ◽

Rough Approximation ◽

Half Filling

Abstract We introduce a family of inhomogeneous XX spin chains whose squared couplings are a polynomial of degree at most four in the site index. We show how to obtain an asymptotic approximation for the Rényi entanglement entropy of all such chains in a constant magnetic field at half filling by exploiting their connection with the conformal field theory of a massless Dirac fermion in a suitably curved static background. We study the above approximation for three particular chains in the family, two of them related to well-known quasi-exactly solvable quantum models on the line and the third one to classical Krawtchouk polynomials, finding an excellent agreement with the exact value obtained numerically when the Rényi parameter α is less than one. When α ≥ 1 we find parity oscillations, as expected from the homogeneous case, and show that they are very accurately reproduced by a modification of the Fagotti-Calabrese formula. We have also analyzed the asymptotic behavior of the Rényi entanglement entropy in the non-standard situation of arbitrary filling and/or inhomogeneous magnetic field. Our numerical results show that in this case a block of spins at each end of the chain becomes disentangled from the rest. Moreover, the asymptotic approximation for the case of half filling and constant magnetic field, when suitably rescaled to the region of non-vanishing entropy, provides a rough approximation to the entanglement entropy also in this general case.

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