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Physica E Low-dimensional Systems and Nanostructures

Entanglement in the Heisenberg spin chain with multiple interaction

W. W. Cheng, Chuan-Jia Shan, Yongxian Huang, T.K. Liu, Hao-Tian Li

Published Jul 20, 2010• 10 citations
Publisher
DOI
10.1016/j.physe.2010.07.012

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•Dec 1, 2009•0 citations
The energy level and the eigenstate entanglement in a Heisenberg spin chain with three-spin interaction are analysed.We study the entanglement in a tri-qubit Heisenberg spin chain,the entangled states are all W state.And the ground state entanglement are analysed when the temperature is zero.We find that the entanglement in the antiferromagnetic chain doesn′t change with the parameters.The entanglement in the ferromagnetic chain changes with the anisotropy and three-spin interaction.We also study the thermal entanglement in the system under low temperature.The function of the entanglement is expressed and the relation with temperature,anisotropy and interaction are pictured.
Quantum phase transition in dimerized antiferromagnetic Heisenberg spin chain has been studied. A staircase structure in the variation of concurrence within strongly coupled pairs with that of external magnetic field has been observed indicating multiple critical points. Emergence of entanglement due to external magnetic field or magnetic entanglement is observed for weakly coupled spin pairs in the same dimer chain. Though closed dimerized isotropic XXX Heisenberg chains with different dimer strengths were mainly explored, analogous studies on open chains as well as closed anisotropic (XX interaction) chains with tilted external magnetic field have also been studied.
The Heisenberg spin-chain and the Quantum Kicked Rotor (QKR) are key models in condensed matter and quantum chaos respectively. The former, consisting of a line of qubits that interact with their neighbours through an exchange interaction, has recently received much attention in the context of quantum information and communication. In particular, it has been shown that a Heisenberg chain can be used as a channel for the transfer quantum states and the sharing of entanglement. The QKR, on the other hand, is a paradigm of quantum chaos. It is one of a valuable collection of quantum systems with a well de�ned classical limit that shows both regular and chaotic dynamics. This thesis investigates the dynamics of a Heisenberg chain subjected to periodic ±-kicks from a parabolic magnetic �eld. It will be shown that, when perturbed in this way, spin-chains can provide realizations of QKR systems. Using this connection, well-known features of the dynamics of kicked rotors can be used to manipulate the evolution of excitations and entanglement in the spin-chain. Conversely, results from the spin-chain analysis can inform our knowledge of the kicked rotor systems. The focus of the �rst part of this thesis is the dynamics of singly excited chains. In this case, the kicked Heisenberg chain is shown to be dynamically equivalent to a QKR. Similar correspondences can be found. Two examples, spin-chain realizations of the Double-Kicked Rotor and a double-well kicked rotor, are explored. Later sections are concerned with the dynamics of multiple excitations. These excitations interact - scattering or forming bound states of inverted spins. The kicked chain now corresponds to a system of coupled kicked rotors. It will be shown that by tuning the parameters it is possible to control the time-evolution of correlations in the chain.