Logarithmic delocalization of end spins in the S= 3 2 antiferromagnetic Heisenberg chain

G. Fáth, O. Legeza, Péter Lajkó, F. Iglói

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Abstract

Using the DMRG method we calculate the surface spin correlation function, CL (l) = Slz S L+1-l z, in the spin S= 3 2 antiferromagnetic Heisenberg chain. For comparison we also investigate the S= 1 2 chain with S=1 impurity end spins and the S=1 chain. In the half-integer spin models the end-to-end correlations are found to decay to zero logarithmically, CL (1) ∼ (log L)-2d, with d=0.13 (2). We find no surface order, in clear contrast with the behavior of the S=1 chain, where exponentially localized end spins induce finite surface correlations. The lack of surface order implies that end spins do not exist in the strict sense. However, the system possesses a logarithmically weakly delocalizing boundary excitation, which, for any chain lengths attainable numerically or even experimentally, creates the illusion of an end spin. This mode is responsible for the first gap, which vanishes asymptotically as Δ1 ≈ (π vS d) (L ln L), where vS is the sound velocity and d is the logarithmic decay exponent. For the half-integer spin models our results on the surface correlations and on the first gap support universality. Those for the second gap are less conclusive, due to strong higher-order corrections.

Original languageEnglish
Article number214447
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume73
Issue number21
DOIs
Publication statusPublished - 2006

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Acoustic wave velocity
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decay
acoustic velocity
exponents
impurities
excitation

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

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abstract = "Using the DMRG method we calculate the surface spin correlation function, CL (l) = Slz S L+1-l z, in the spin S= 3 2 antiferromagnetic Heisenberg chain. For comparison we also investigate the S= 1 2 chain with S=1 impurity end spins and the S=1 chain. In the half-integer spin models the end-to-end correlations are found to decay to zero logarithmically, CL (1) ∼ (log L)-2d, with d=0.13 (2). We find no surface order, in clear contrast with the behavior of the S=1 chain, where exponentially localized end spins induce finite surface correlations. The lack of surface order implies that end spins do not exist in the strict sense. However, the system possesses a logarithmically weakly delocalizing boundary excitation, which, for any chain lengths attainable numerically or even experimentally, creates the illusion of an end spin. This mode is responsible for the first gap, which vanishes asymptotically as Δ1 ≈ (π vS d) (L ln L), where vS is the sound velocity and d is the logarithmic decay exponent. For the half-integer spin models our results on the surface correlations and on the first gap support universality. Those for the second gap are less conclusive, due to strong higher-order corrections.",
author = "G. F{\'a}th and O. Legeza and P{\'e}ter Lajk{\'o} and F. Igl{\'o}i",
year = "2006",
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AU - Fáth, G.

AU - Legeza, O.

AU - Lajkó, Péter

AU - Iglói, F.

PY - 2006

Y1 - 2006

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AB - Using the DMRG method we calculate the surface spin correlation function, CL (l) = Slz S L+1-l z, in the spin S= 3 2 antiferromagnetic Heisenberg chain. For comparison we also investigate the S= 1 2 chain with S=1 impurity end spins and the S=1 chain. In the half-integer spin models the end-to-end correlations are found to decay to zero logarithmically, CL (1) ∼ (log L)-2d, with d=0.13 (2). We find no surface order, in clear contrast with the behavior of the S=1 chain, where exponentially localized end spins induce finite surface correlations. The lack of surface order implies that end spins do not exist in the strict sense. However, the system possesses a logarithmically weakly delocalizing boundary excitation, which, for any chain lengths attainable numerically or even experimentally, creates the illusion of an end spin. This mode is responsible for the first gap, which vanishes asymptotically as Δ1 ≈ (π vS d) (L ln L), where vS is the sound velocity and d is the logarithmic decay exponent. For the half-integer spin models our results on the surface correlations and on the first gap support universality. Those for the second gap are less conclusive, due to strong higher-order corrections.

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