Entanglement across extended random defects in the XX spin chain. (23rd August 2017) - Juhász, Róbert
Abstract: We study the half-chain entanglement entropy in the ground state of the spin-1/2 XX chain across an extended random defect, where the strength of disorder decays with the distance from the interface algebraically as Δ l ∼ l − κ . In the whole regime κ ⩾ 0, the average entanglement entropy is found to increase logarithmically with the system size L as S L ≃ c e f f ( κ ) 6 ln ⁡ L + c o n s t, where the effective central charge c e f f ( κ ) depends on κ . In the regime κ < 1 / 2, where the extended defect is a relevant perturbation, the strong-disorder renormalization group method gives c e f f ( κ ) = ( 1 − 2 κ ) ln ⁡ 2, while, in the regime κ ⩾ 1 / 2, where the extended defect is irrelevant in the bulk, numerical results indicate a non-zero effective central charge, which increases with κ . The variation of c e f f ( κ ) is thus found to be non-monotonic and discontinuous at κ = 1 / 2 .