Random antiferromagnetic quantum spin chains: Exact results from scaling of rare regions
Random antiferromagnetic quantum spin chains: Exact results from scaling of rare regions
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随机反铁磁量子自旋链：稀有区域缩放的精确结果
DOI：
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发表时间：
1999
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影响因子：
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通讯作者：
Heiko Rieger
中科院分区：
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作者：
F. Iglói;R. Juhász;R. Juhász;Heiko Rieger
我们通过分析和数值方法以及缩放考虑，研究具有随机交换耦合的 XY 和二聚 XX 自旋 1/2 链。我们将之前的研究扩展到动力学特性、表面量和操作员概况，并对格里菲斯相进行了详细分析。我们提出了一种基于稀有区域的标度特性的平均量唯象标度理论，其中耦合的分布遵循幸存的随机游走特征。利用这一理论，我们获得了随机 XY 和 XX 模型的完整临界衰减指数（无论是在体积还是在表面）。缩放结果面临基于自由费米子映射的数值计算，然后导致与有向游走的精确对应。发现大型有限系统（L <= 512）上的数值计算关键算子轮廓遵循现象学标度理论的衰减指数的共形预测。临界状态下的动态相关性平均对数缓慢，并且其分布呈现多尺度特征。在格里菲斯阶段，它是非临界区域的扩展部分，平均自相关具有非通用衰减指数的幂律形式，这是通过分析计算得出的。我们注意到我们的工作扩展到随机反铁磁 XXZ 链和更高维度。
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 confronted with 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 conformal predictions with the decay exponents of the phenomenological scaling theory. Dynamical correlations in the critical state are in average logarithmically slow and their distribution show multi-scaling character. In the Griffiths phase, which is an extended part of the off-critical region average autocorrelations have a power-law form with a non-universal decay exponent, which is analytically calculated. We note on extensions of our work to the random antiferromagnetic XXZ chain and to higher dimensions.