Entanglement in many-body systems

Abstract

The recent interest in aspects common to quantum information and condensed matter has prompted a flory of activity at the border of these disciplines that were far distant untill few years ago. Numerous interesting questions have been addressed so far. Here we review an important part of this field, the properties of the entanglement in many-body systems. We discuss the zero and finite temperature properties of entanglement in interacting spin, fermion and boson model systems. Both bipartite and multipartite entanglement will be considered. In equilibrium we show how entanglement is tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium we discuss how to generate and manipulate entangled states by means of many-body Hamiltonians.

Entanglement switching via the Kondo effect in triple quantum dots

“…Even for extremely large values of fluctuations δn 2 C , the concurrence C AB remains constant above Γ c . Charge fluctuations δn 2 A remain low for the whole range of Γ , as expected.…”

“…Results presented in Figures 2h-2n are thus analogous to those in Figures 2a-2g. The main distinction is the fact that dots A and B remain consistently decoupled from the rest of the system for the whole range of Γ , as is particularly clearly seen from the spin-spin correlations signaling triplet or singlet state for Γ < Γ c and Γ > Γ c , respectively, while S A · S C ∼ 0 due to the increase of δn 2 C with increasing Γ/D. Even for extremely large values of fluctuations δn 2 C , the concurrence C AB remains constant above Γ c .…”

“…Creation of entangled states is essential for quantum computation and communication where most qubit operations cannot be performed through the manipulation of separable states [1][2][3][4]. Two electron spin qubits, each localized in one of two adjacent semiconductor quantum dots (QDs), can be coupled via the Heisenberg exchange interaction due to virtual electron tunneling between the dots [5,6].…”

Multipoint entanglement in disordered systems

“…By contrast, temporal evolution of quantum information has not been thoroughly classified. In recent years, closely related properties, such as von Neumann and Renyi bipartite entanglement entropies of subsystems of isolated many-body systems have received serious attention, especially regarding its area-law behavior in the ground state [4][5][6][7][8] and its possible deviations [9][10][11] . One prominent result is the (LiebRobinson) linear in-time growth of entanglement in ballistic and diffusive systems 12 .…”

Unified scheme for correlations using linear relative entropy

“…Besides its fundamental aspects, entanglement is commonly accepted of paramount importance in the development of quantum information science [1,2,3,4,5,6]. In fact, entangled states have found various applications in quantum information processing protocols as for instance quantum cryptography [7], quantum teleportation [8], quantum dense coding [9].…”