Divergence of the entanglement range in low-dimensional quantum systems

Abstract

We study the pairwise entanglement close to separable ground states of a class of one dimensional quantum spin models. At T=0 we find that such ground states separate regions, in the space of the Hamiltonian parameters, which are characterized by qualitatively different types of entanglement, namely parallel and antiparallel entanglement; we further demonstrate that the range of the Concurrence diverges while approaching separable ground states, therefore evidencing that such states, with uncorrelated fluctuations, are reached by a long range reshuffling of the entanglement. We generalize our results to the analysis of quantum phase transitions occurring in bosonic and fermionic systems. Finally, the effects of finite temperature are considered: At T >0 we evidence the existence of a region where no pairwise entanglement survives, so that entanglement, if present, is genuinely multipartite.

Entanglement and level crossings in frustrated ferromagnetic rings

“…This tunable distance is quite different from the 'entanglement range' of Ref. [47]; our concurrences are not decaying with distance but are nonzero only at a certain distance. Fig.…”

“…In the XYZ model in a magnetic field, the concurrence extends to several lattice sites, but still has finite range [50]. Long-range concurrences are rare; the known examples correspond to specific phase transitions [47] or to carefully constructed models and geometries [48,49].…”

Quantum discord and classical correlations in the bond-charge Hubbard model: Quantum phase transitions, off-diagonal long-range order, and violation of the monogamy property for discord

“…Therefore, in the central region of phase I, where K i,j vanishes ∀|i − j| > 1, two-point discord and classical correlations are still present. Correlations are modulated by the sinusoidal behavior induced by Γ ij and at fixed µ they all decay algebraically with the distance: In proximity of the transition I → IV it was shown in 35 that the system exhibits an entanglement transition 9 : the range of the entanglement R K , i.e., the maximal distance |i − j| for which K i,j = 0, goes to infinity when approaching the transition. In particular, K i,j have a maximum value for n s → 1 as |i − j| → ∞.…”

“…On the other side, quantum information theory has provided novel and deep insights into the physics of condensed-matter systems. In particular, since the capability of entanglement to mark quantum phase transitions (QPT) was first recognized 5,6 , the concept of quantum correlations has become essential in characterizing quantum critical phenomena [7][8][9][10][11][12] . In this context, quantum correlations and entanglement have been usually identified as one and the same concept.…”

AnisotropicXYmodel on the inhomogeneous periodic chain

“…Important results of this application can be found in the recent work by Amico et al [8] and in the references therein.…”