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arXiv:cond-mat/0210002

Reply to the "Comment on 'Neel order in doped quasi one-dimensional antiferromagnets'"

Sebastian Eggert, Ian K. Affleck, Matthew D. P. Horton

Published Sep 30, 2002• 0 citations
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Abstract

In a recent comment by A.A. Zvyagin to our Letter [Phys. Rev. Lett. 89, 47202 (2002)] it was pointed out that the bosonization treatment of the antiferromagnetic Heisenberg chain is only valid in the low temperature and long length limit. We support this statement and quantify the limits of validity by explicitly showing the crossover to the high temperature and/or short length limit using a combination of bosonization formulas and numerical results.

DOI
10.48550/arxiv.cond-mat/0210002

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In a recent comment by A.A. Zvyagin to our Letter [Phys. Rev. Lett. 89, 47202 (2002)] it was pointed out that the bosonization treatment of the antiferromagnetic Heisenberg chain is only valid in the low temperature and long length limit. We support this statement and quantify the limits of validity by explicitly showing the crossover to the high temperature and/or short length limit using a combination of bosonization formulas and numerical results.
In their Comment Giraud and Combescot (GC) [Phys. Rev. A 82, 037603 (2010)] point out that the contribution to the impurity-boson distribution function ${\ensuremath{\rho}}_{\mathit{bi}}(x\ensuremath{-}y)$ of a term we dropped is not negligible, rather than being negligible in the thermodynamic limit as we had conjectured. We now agree with them, but our results for ${\ensuremath{\rho}}_{\mathit{bi}}$ are highly accurate for large impurity-boson mass ratio mi/m{m}_{i}/mmi​/m, for all values of $x\ensuremath{-}y$ and boson-impurity coupling constant.
Critical temperature of quasi-one-dimensional general-spin Ising ferromagnets is investigated by means of the cluster Monte Carlo method performed on infinite-length strips, $L\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$ or $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$. We find that in the weak interchain coupling regime the critical temperature as a function of the interchain coupling is well-described by a chain mean-field formula with a reduced effective coordination number, as the quantum Heisenberg antiferromagnets recently reported by Yasuda et al. [Phys. Rev. Lett. 94, 217201 (2005)]. It is also confirmed that the effective coordination number is independent of the spin size. We show that in the weak interchain coupling limit the effective coordination number is, irrespective of the spin size, rigorously given by the quantum critical point of a spin-1∕21∕21∕2 transverse-field Ising model.