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The European Physical Journal B

Spin chains with nearest and next nearest neighbour interactions

Walter Selke

Published Mar 1, 1977• 18 citations
Publisher
DOI
10.1007/bf01315508

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By using the method of density-matrix renormalization-group to solve the different spin–spin correlation functions, the nearest-neighbouring entanglement (NNE) and the next-nearest-neighbouring entanglement (NNNE) of one-dimensional alternating Heisenberg XY spin chain are investigated in the presence of alternating the-nearest-neighbouring interaction of exchange couplings, external magnetic fields and the next-nearest neighbouring interaction. For a dimerised ferromagnetic spin chain, the NNNE appears only above a critical dimerized interaction, meanwhile, the dimerized interaction a effects a quantum phase transition point and improves the NNNE to a large extent. We also study the effect of ferromagnetic or antiferromagnetic next-nearest neighbouring (NNN) interaction on the dynamics of NNE and NNNE. The ferromagnetic NNN interaction increases and shrinks the NNE below and above a critical frustrated interaction respectively, while the antiferromagnetic NNN interaction always reduces the NNE. The antiferromagnetic NNN interaction results in a large value of NNNE compared with the case where the NNN interaction is ferromagnetic.

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arXiv:1902.00688•Journal of Physics A Mathematical and Theoretical•Jan 10, 2020•2 citations
By using the method of density-matrix renormalization-group to solve the different spin–spin correlation functions, the nearest-neighbouring entanglement (NNE) and the next-nearest-neighbouring entanglement (NNNE) of one-dimensional alternating Heisenberg XY spin chain are investigated in the presence of alternating the-nearest-neighbouring interaction of exchange couplings, external magnetic fields and the next-nearest neighbouring interaction. For a dimerised ferromagnetic spin chain, the NNNE appears only above a critical dimerized interaction, meanwhile, the dimerized interaction a effects a quantum phase transition point and improves the NNNE to a large extent. We also study the effect of ferromagnetic or antiferromagnetic next-nearest neighbouring (NNN) interaction on the dynamics of NNE and NNNE. The ferromagnetic NNN interaction increases and shrinks the NNE below and above a critical frustrated interaction respectively, while the antiferromagnetic NNN interaction always reduces the NNE. The antiferromagnetic NNN interaction results in a large value of NNNE compared with the case where the NNN interaction is ferromagnetic.
Abstract An integrable anisotropic Heisenberg spin chain with nearest-neighbour couplings, next-nearest-neighbour couplings and scalar chirality terms is constructed. After proving the integrability, we obtain the exact solution of the system. The ground state and the elementary excitations are also studied. It is shown that the spinon excitation of the present model possesses a novel triple arched structure. The elementary excitation is gapless if the anisotropic parameter is real while the elementary excitation has an enhanced gap by the next-nearest-neighbour and chiral three-spin interactions if the anisotropic parameter is imaginary. The method of this paper provides a general way to construct integrable models with next-nearest-neighbour interactions.