Random antiferromagnetic quantum spin chains: Exact results from scaling of rare regions

F. Iglói, Róbert Juhász, Heiko Rieger

Research output: Contribution to journalArticle

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Abstract

We study XY and dimerized XX spin-1/2 chains with random exchange couplings by analytical and numerical methods and scaling considerations. We extend previous investigations to dynamical properties, to surface quantities, and operator profiles, and give a detailed analysis of the Griffiths phase. We present a phenomenological scaling theory of average quantities based on the scaling properties of rare regions, in which the distribution of the couplings follows a surviving random-walk character. Using this theory we have obtained the complete set of critical decay exponents of the random XY and XX models, both in the volume and at the surface. The scaling results are confirmed by numerical calculations based on a mapping to free fermions, which then lead to an exact correspondence with directed walks. The numerically calculated critical operator profiles on large finite systems (L≤512) are found to follow conformai predictions with the decay exponents of the phenomenological scaling theory. Dynamical correlations in the critical state are in average logarithmically slow and their distribution shows multiscaling character. In the Griffiths phase, which is an extended part of the off-critical region, average autocorrelations have a power-law form with a nonuniversal decay exponent, which is analytically calculated. We note on extensions of our work to the random antiferromagnetic XXZ chain and to higher dimensions.

Original languageEnglish
Pages (from-to)11552-11568
Number of pages17
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume61
Issue number17
Publication statusPublished - 2000

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scaling
Exchange coupling
Fermions
Autocorrelation
exponents
Numerical methods
decay
operators
profiles
random walk
autocorrelation
fermions
predictions

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Random antiferromagnetic quantum spin chains : Exact results from scaling of rare regions. / Iglói, F.; Juhász, Róbert; Rieger, Heiko.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 61, No. 17, 2000, p. 11552-11568.

Research output: Contribution to journalArticle

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