Sublogarithmic behaviour of the entanglement entropy in fermionic chains

Abstract

In this paper, we discuss the possibility of unexplored behaviours for the entanglement entropy in extended quantum systems. Namely, we study the Rényi entanglement entropy for the ground state of long-range Kitaev chains with slow decaying couplings. We obtain that, under some circumstances, the entropy grows sublogarithmically with the length of the subsystem. Our result is based on the asymptotic behaviour of a new class of Toeplitz determinants whose symbol does not lie within the application domain of the Strong Szegő Theorem or the Fisher-Hartwig conjecture.

arXiv comment30 pages, 4 figures, 1 table. Final version to appear in JSTAT. One new figure. Some comments and references added

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Cited by in corpus (8)

• Symmetry-resolved entanglement in a long-range free-fermion chain
• Volume-law to area-law entanglement transition in a non-unitary periodic Gaussian circuit
• Logarithmic entanglement scaling in dissipative free-fermion systems
• Mimicking quantum correlation of a long-range Hamiltonian by finite-range interactions
• On the complex behaviour of the density in composite quantum systems
• Entanglement of weighted graphs uncovers transitions in variable-range interacting models
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping
• Asymptotic behaviour of determinants through the expansion of the Moyal star product