arXiv:0707.0266v2 [cond-mat.other] 5 Nov 2007 Increasing entanglement through engineered disorder in the random Ising chain D. Binosi, 1, ∗ G. De Chiara, 2, † S. Montangero, 3, ‡ and A. Recati 2, § 1 European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*), Villa Tambosi, Strada delle Tabarelle 286, I-38050 Villazzano (TN) Italy 2 BEC-CNR-INFM & Phisics Department, University of Trento, Via Sommarive 14, I-38050 Povo (TN) Italy 3 NEST-CNR-INFM & Scuola Normale Superiore, P.zza dei Cavalieri 7 56126 Pisa Italy (Dated: April 19, 2009) The ground state entanglement entropy between block of sites in the random Ising chain is studied by means of the Von Neumann entropy. We show that in presence of strong correlations between the disordered couplings and local magnetic fields the entanglement increases and becomes larger than in the ordered case. The different behavior with respect to the uncorrelated disordered model is due to the drastic change of the ground state properties. The same result holds also for the random 3-state quantum Potts model. PACS numbers: 75.10.Pq; 03.67.Mn; 75.10.Nr Entanglement plays a central role in modern quan- tum mechanics. Having been regarded for long time as the root of the incompleteness of quantum mechan- ics and the source of several paradoxes [1], with the ad- vent of Quantum Information (QI) theory it has received renewed attention, and acquired the status of a funda- mental resource for QI processing [2]. In the context of strongly correlated quantum systems entanglement arises in a natural way [3], and can in fact be regarded as a conceptual bridge between condensed matter physics and QI theory. In particular, much attention has been recently devoted to the ground state entanglement be- tween two blocks of spins in one dimensional spin chains [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. By means of both analytical proofs and numerical simulations, this quan- tity has been shown to be logarithmically divergent with the length of the block when the spin chain is critical. Re- markably, the prefactor of the logarithm is proportional to the central charge of the corresponding conformal field theory (CFT) associated with the spin model at hands [16]. The average block entropy has been also studied in the context of random critical spin chains[12, 17, 18, 19, 20, 21, 22]. In this case, on the one hand works on random Ising and XXZ spin 1/2 chains [12, 17, 18] suggest that the block entropy still grows logarithmically with the size of the block but with a smaller prefactor of the logarithm with respect to the ordered model, being “renormalized” by a factor ln 2. On the other hand, the block entropy in random quantum Potts chains with spin dimension d ≥ 2 has been studied in [19], where a strong-disorder renor- malization group (RG) analysis shows that the average entropy still diverges logarithmically but that the pref- actor of the entropy is not proportional to the one of the * Electronic address: binosi@ect.it † Electronic address: dechiara@science.unitn.it ‡ Electronic address: monta@sns.it § Electronic address: recati@science.unitn.it corresponding pure model and becomes larger than the latter when d> 41. This provides evidence that disorder can increase entanglement with respect to pure models, contrary to na¨ ıve expectations. The same analysis have been performed in aperiodic spin 1/2 chains and again it has been shown that the prefactor of the entropy log- arithmic scaling is not simply the “renormalized” factor of the homogeneous model [23]. Therefore at present the possibility of associating an effective central charge to a non-homogeneous system is unclear. In this work we study a random critical Ising spin chain [24] where the (nearest neighbor) couplings and the lo- cal transverse magnetic field are drawn from the same probability distribution and in addition share a certain (tunable) degree of correlation. We compute the average block entropy for this model and show that the prefac- tor of the entropy in a class of random correlated chain is larger than in the homogeneous case. An analogous result is found to hold also for larger dimension as we demonstrate in the random correlated quantum Potts model with d = 3. We consider a spin chain with open boundary condi- tions and with d states |0〉, |1〉,..., |d − 1〉 per lattice site, described by the Hamiltonian [25] H d = − L−1  i=1 J i d−1  n=1 ( ¯ S z i S z i+1 ) n − L  i=1 h i d−1  n=1 Γ n i . (1) Here L is the length of the chain, Γ represents the ladder operator Γ|s〉 = |(s +1) mod d〉, 〈k| S z |k ′ 〉 = e 2iπk/d δ kk ′ (k,k ′ =0,...,d − 1) and ¯ S z is the hermitian conjugate of S z . For d = 2, S z ≡ σ z (with σ (x,y,z) the Pauli matrices) and the model reduces to the (random) transverse field Ising model H 2 = − L−1  i=1 J i σ z i σ z i+1 − L  i=1 h i σ x i . (2) In the pure case J i = h i = 1 while in the random case J i and h i are positive random numbers drawn from a joint