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arXiv 1603.09548hep-lat
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QCD手性跃迁的类Anderson模型

An Anderson-like model of the QCD chiral transition

Matteo Giordano, Tamas G. Kovacs, Ferenc Pittler

摘要:

本文将格点狄拉克算符看作随机哈密顿量,研究了有限温度QCD中的手征对称性破缺和本征模局域化问题。我们将交错的狄拉克算符转换为非传统的三维安德森哈密顿量(“狄拉克-安德森哈密顿量”),它带有内部自由度,由规范链的波动提供无序。在这个框架中,我们确定的功能相关的手征对称性恢复和本地化的低位置的狄拉克本征模在订购的本地Polyakov线,并在相关的空间链接之间的相关性跨越时间片,从而将这两种现象的解除禁闭过渡。然后,我们建立了一个玩具模型的基础上QCD和狄拉克-安德森方法,取代Polyakov线与自旋变量和简化的空间规范链接的动力学,但保留上述相关的动力学特征。我们的玩具模型成功地再现了QCD谱的主要特征和狄拉克本征模的手征对称性破坏和本地化,无论是在有序(deconfined)和无序(限制)阶段。此外,它使我们能够分别研究Dirac-Anderson哈密顿量的对角项和非对角项在这两种现象中所起的作用。我们的研究结果支持我们的预期,手征对称性恢复和本地化的低模式是密切相关的,这两者都是由解除禁闭过渡。

英文摘要:

We study the problems of chiral symmetry breaking and eigenmode localisation in finite-temperature QCD by looking at the lattice Dirac operator as a random Hamiltonian. We recast the staggered Dirac operator into an unconventional three-dimensional Anderson Hamiltonian ("Dirac-Anderson Hamiltonian") carrying internal degrees of freedom, with disorder provided by the fluctuations of the gauge links. In this framework, we identify the features relevant to chiral symmetry restoration and localisation of the low-lying Dirac eigenmodes in the ordering of the local Polyakov lines, and in the related correlation between spatial links across time slices, thus tying the two phenomena to the deconfinement transition. We then build a toy model based on QCD and on the Dirac-Anderson approach, replacing the Polyakov lines with spin variables and simplifying the dynamics of the spatial gauge links, but preserving the above-mentioned relevant dynamical features. Our toy model successfully reproduces the main features of the QCD spectrum and of the Dirac eigenmodes concerning chiral symmetry breaking and localisation, both in the ordered (deconfined) and disordered (confined) phases. Moreover, it allows us to study separately the roles played in the two phenomena by the diagonal and the off-diagonal terms of the Dirac-Anderson Hamiltonian. Our results support our expectation that chiral symmetry restoration and localisation of the low modes are closely related, and that both are triggered by the deconfinement transition.

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