Remarks on the Sachdev-Ye-Kitaev model
Remarks on the Sachdev-Ye-Kitaev model
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DOI：
10.1103/physrevd.94.106002
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发表时间：
2016-11-04
影响因子：
5
通讯作者：
Stanford, Douglas
中科院分区：
文献类型：
--
作者：
Maldacena, Juan;Stanford, Douglas
我们研究了Sachdev，Ye和Kitaev提出的量子力学模型。该模型由N马约拉纳费米子与随机相互作用的几个费米子在同一时间。它在大N极限下是易处理的，其中经典变量是双局域费米子双线性。该模型在低能量下变得强相互作用，在那里它发展出一种涌现的共形对称性。我们研究了基本费米子的二点和四点函数。这提供了双局域场的物理激发谱。涌现共形对称是一种重新参数化对称，它自发破缺为SL（2，R），导致零模。这些零模式被一个小的残余显式破缺所提升，这对四点函数产生了增强的贡献。这一贡献显示了最大的李雅普诺夫指数在混沌区域（出的时间有序相关器）。我们期望这些特征是具有涌现重参数化对称性的大N量子力学系统的普适性质。这篇文章主要是基于Kitaev的谈话，这促使我们制定出那里描述的想法的细节。
We study a quantum-mechanical model proposed by Sachdev, Ye and Kitaev. The model consists of N Majorana fermions with random interactions of a few fermions at a time. It it tractable in the large-N limit, where the classical variable is a bilocal fermion bilinear. The model becomes strongly interacting at low energies where it develops an emergent conformal symmetry. We study two-and four-point functions of the fundamental fermions. This provides the spectrum of physical excitations for the bilocal field. The emergent conformal symmetry is a reparametrization symmetry, which is spontaneously broken to SL(2,R), leading to zero modes. These zero modes are lifted by a small residual explicit breaking, which produces an enhanced contribution to the four-point function. This contribution displays a maximal Lyapunov exponent in the chaos region (out-of-time-ordered correlator). We expect these features to be universal properties of large-N quantum mechanics systems with emergent reparametrization symmetry. This article is largely based on talks given by Kitaev, which motivated us to work out the details of the ideas described there.