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arXiv:cond-mat/0308589 · Journal of the Physical Society of Japan

Next Nearest-Neighbor Correlation Functions of the Spin-1/2XXZChain at Massive Region

Minoru Takahashi, Go Kato, Masahiro Shiroishi

Published Jan 15, 2004• 31 citations
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Abstract

The second neighbor correlation functions of the spin-${1/2}$ $XXZ$ chain in the ground state are expressed in the form of three dimensional integrals. We show that these integrals can be reduced to one-dimensional ones and thereby evaluate the values of the next nearest-neighbor correlation functions for ${Δ>1}$.

DOI
10.1143/jpsj.73.245

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The correlation functions of the spin-1/2 XXZ spin chain in the ground state are expressed in the form of the multiple integrals. For -1< Delta <1, they were obtained by Jimbo and Miwa in 1996. Especially the next nearest-neighbour correlation functions are given as certain three-dimensional integrals. We shall show these integrals can be reduced to one-dimensional ones and thereby evaluate the values of the next nearest-neighbor correlation functions. We have also found that the remaining one-dimensinal integrals can be evaluated analytically, when nu = arccos(Delta)/pi is a rational number.
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The features of the concurrences between the nearest-neighbors and that of the next-nearest-neighbors for the one-dimensional Heisenberg model with next-nearest-neighbor coupling JJJ are studied as functions of temperature and JJJ. The two concurrences exhibit a different dependence on JJJ at the ground state, which could be interpreted from the point of view of the correlation functions. The threshold temperature at which the concurrence is zero and the temperature effect on the two concurrences for systems up to 12 sites are studied numerically.
We study the one-dimensional Hubbard model with next-nearest-neighbor hopping by means of the numerical diagonalization for finite-size clusters. It is found that the ground state is evidently partially spin-polarized in a wide region of intermediate values of on-site Coulomb repulsion, which provides the first example as a minimal model without orbital degeneracy. Analysis of correlation functions makes it clear that the partially spin-polarized states form a spin polaron. Polaron's size grows with the increasing interaction.