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arXiv 1503.05732cond-mat.stat-mechmath-phmath.MP
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随机矩阵理论与量子自旋链中的临界现象

Random matrix theory and critical phenomena in quantum spin chains

J. Hutchinson, J. P. Keating, F. Mezzadri

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14 pages
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摘要：

本文计算了一类量子自旋链的临界性质，这类量子自旋链在Fermi算符中是二次的，并且在与经典紧群$U(N)$，$O(N)$和$Sp(2N)$有关的某些对称性约束下可以精确求解.特别地，我们计算了临界指数$s$、$ν$和$z$，分别对应于能隙、关联长度和动力学指数。我们还计算了基态量子点$\left\langle σ^{x}_{i} σ^{x}_{i+n} \right\rangle_{g}$、$\left\langle σ^{y}_{i} σ^{y}_{i+n} \right\rangle_{g}$和$\left\langle \prod^{n}_{i=1} σ^{z}_{i} \right\rangle_{g}$，它们都表现出准长程序，其临界指数依赖于系统参数.我们的方法建立了普遍性的指数类系统的问题。

英文摘要：

We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups $U(N)$, $O(N)$ and $Sp(2N)$. In particular we calculate critical exponents $s$, $ν$ and $z$, corresponding to the energy gap, correlation length and dynamic exponent respectively. We also compute the ground state correlators $\left\langle σ^{x}_{i} σ^{x}_{i+n} \right\rangle_{g}$, $\left\langle σ^{y}_{i} σ^{y}_{i+n} \right\rangle_{g}$ and $\left\langle \prod^{n}_{i=1} σ^{z}_{i} \right\rangle_{g}$, all of which display quasi-long-range order with a critical exponent dependent upon system parameters. Our approach establishes universality of the exponents for the class of systems in question.

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