Characterizing entanglement by momentum jump in the frustrated Heisenberg ring at a quantum phase transition

Abstract

We study the pairwise concurrences, a measure of entanglement, of the ground states for the frustrated Heisenberg ring to explore the relation between entanglement and quantum phase transition associated with the momentum jump. The groundstate concurrences between any two sites are obtained analytically and numerically. It shows that the summation of all possible pairwise concurrences is an appropriate candidate to depict the phase transition. We also investigate the role that the momentum takes in the jump of concurrence at the critical points. We find that an abrupt momentum change rusults in the maximal concurrence difference of two degenerate ground states.

The Peierls distorted chain as a quantum data bus for quantum state transfer

“…State |n − , n + is the ground or first excited states of the whole system (the Hamiltonian (11) with g = 0), which are spanned by the states possessing the same parity as the states |n − , n + ; 0 = |n − , n + AB ⊗ |0 SSH . On the other hand, it is known that the eigenstates of H AB with unity concurrence are maximally entangled states [16,17]. Thus by calculating the mode concurrences of two sites A and B for the ground and first excited states of the total system (11), one can verify whether the exact solutions can be well approximated by that from the effective Hamiltonian.…”

Concurrence in collective models

“…An important issue is to understand how the structure of the ground state is affected by the existence of a critical point. The first answers came with the study of one-dimensional spin systems [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21] where a strong interplay between QPTs and the variation of the entanglement with the control parameters has been in evidence. However, a complete classification of the possible scenarios likely to arise depending on the nature of the transitions is still lacking [22,23].…”

Relation between two measures of entanglement in spin-1∕2and spinless fermion quantum chain systems

“…It plays a fundamental role in quantum information processing (QIP) schemes and quantum computing, thus is regarded as an important resource for these technologies [1]. It also has been demonstrated that the quantum entanglement can be used to realize quantum teleportation [2,3,4,5], as well as to characterize the quantum critical phenomena in strongly correlated systems [6,7,8,9,10].…”