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.

Symmetry-resolved entanglement in a long-range free-fermion chain

“…For instance, in that case, the ground state entanglement entropy may display a logarithmic growth even if the mass gap is not zero, as occurs in the long-range Kitaev chain [16][17][18][19]. In general, other more exotic behaviours may arise, depending on the specific form of the couplings [20]. The theoretical study of long-range systems has also been stimulated by the development of experimental techniques that allow to simulate them in a laboratory [21][22][23][24].…”

Symmetry-resolved entanglement in a long-range free-fermion chain

“…In this case, the restriction V A is a L × L block Toeplitz matrix with symbol the 2 × 2 matrix G(θ) of Eq. (20). To deduce the large L behaviour of D A (λ) and, therefore, of the charged moments Z (n) A (α), we will apply the results on the asymptotic behaviour of block Toeplitz determinants obtained in Ref.…”

Entanglement and Correlation Spreading in non-Hermitian Spin Chains

“…In this limit, we have Π l I l (∞) • σ. In full analogy to other systems considered in the literatures [54][55][56][57], the subleading term is logarithmic in and can be computed following the guidelines in Ref. [48].…”

“…Stationary state Entanglement Entropy -Finally, we compute analytically the entanglement entropy of the stationary state in the thermodynamic limit and for a large interval 1. The key insight is that for our non-Hermitian spin chain, much like for critical ground-state systems [48,[54][55][56][57], the leading behavior of the entanglement is controlled by the presence of singularities in Π ∞ (k) ≡ Π ∞ (k) • σ (cfr. Eq.…”