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Physica B Condensed Matter

Quantum entanglement investigation on impurity effects in the transverse Ising chain

Xuchu Huang, Tieyan Si, Zhihua Yang

Published Jan 14, 2015• 3 citations
Publisher
DOI
10.1016/j.physb.2015.01.007

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Using a T=0 real-space renormalisation-group method, the spontaneous magnetisation is calculated on an impurity site of the quantum spin- 1 / 2 Ising chain in a transverse field. Two kinds of impurities are considered: either a transverse field or a bond is different from its host value. In both cases the magnetisation vanishes at the critical field with an exponent beta 0 different from the host exponent and varying continuously with the impurity field (or impurity bond). These results agree with recent exact investigations of equivalent classical two-dimensional models.
Using the method of the Jordan–Wigner transformation for solving different spin–spin correlation functions, we have investigated the generation of next-nearest-neighbouring entanglement in a one-dimensional quantum Ising spin chain with the Gaussian distribution impurities of exchange couplings and external magnetic fields taken into account. The maximal value of entanglement between the next-nearest-neighbouring qubits in the transverse Ising model was analysed in detail by varying the effectively controlled parameters such as interchange coupling, magnetic field and the system impurity. For such systems, where both exchange couplings and external magnetic field disorder appear, we show that it is possible to achieve next-nearest-neighbouring entanglement better than the previously discussed pure Ising spin chain case. We also show that the Gaussian distribution impurity can induce next-nearest-neighbouring entanglement, which can be used as a means to characterize quantum phase transition.