一维任意子模型中的非对角相关：一种副本方法

On the replica structure of Sachdev-Ye-Kitaev model

We investigate existence of replica off-diagonal solutions in the field-theoretical description of Sachdev-Ye-Kitaev model. To this end we evaluate a set of local and non-local dynamic correlation functions in the long time limit. We argue that the structure of the soft-mode Schwarzian action is qualitatively different in replica-diagonal vs. replica-off-diagonal scenarios, leading to distinct long-time predictions for the correlation functions. We then evaluate the corresponding correlation functions numerically and compare the simulations with analytical predictions of replica-diagonal and r…

一维链中巡游任意子的分形化

Fractionalization of itinerant anyons in one dimensional chains

我们构建模型的相互作用的巡回非阿贝尔任意子沿一维链移动，特别关注巡回伊辛任意子链，并推导出有效的任意子t-J模型的低能量部门。通过精确对角化解决这些模型，我们发现任意子分解为电荷和（非阿贝尔）任意子自由度-Luttinger液体中发生的电子自旋-电荷分离的概括。激发光谱的详细描述相结合的光谱电荷和任意扇区需要一个微妙的耦合电荷和任意激发之间的微观水平（我们也发现存在于Luttinger液体），尽管宏观分馏。

一维巡游相互作用非阿贝尔任意子

One-dimensional itinerant interacting non-Abelian anyons

我们构造了沿一维链运动的相互作用的巡游非阿贝尔任意子模型。我们研究了与SU（2）_2和SU（2）_3任意子有关的巡游Ising（Majorana）和Fibonacci任意子，它们分别描述了Moore-Read和Z_3-Read-Rezayi分数量子Hall态的准粒子。在导出电子大U有效哈伯德模型的基础上，我们导出了低能区的有效任意子t-J模型。通过精确对角化解决这些模型，我们发现任意子分解为电荷和（中性）任意子自由度-Luttinger液体中发生的电子自旋-电荷分离的概括。激发光谱的详细描述可以通过结合电荷和任意子扇区的光谱来进行。任意子扇区是局域相互作用任意子的压缩链之一，因此可以用相同的共形场论（CFT）来描述，对于伊辛任意子，中心荷c=1/2，对于具有反铁磁或铁磁耦合的斐波那契任意子，c=7/10或c=4/5。电荷扇区是一系列硬核玻色子的光谱，这些玻色子的相移与组合的任意子本征态的动量相一致，揭示了微观水平上电荷和任意子激发之间的微妙耦合（我们也发现存在于Luttinger液体中），尽管宏观分馏。从链段之间的纠缠熵中提取的组合中心电荷为1+c，其中c是局域任意子（压缩）链的基础CFT的中心荷。

Replica-nondiagonal solutions in the SYK model

We study the SYK model in the large $N$ limit beyond the replica-diagonal approximation. First we show that there are exact replica-nondiagonal solutions of the saddle point equations for $q=2$ for any finite replica number $M$. In the interacting $q=4$ case we are able to construct the numerical solutions, which are in one-to-one correspondence to the analytic solutions of the quadratic model. These solutions are singular in the $M \to 0$ limit in both quadratic and quartic interaction cases. The calculations of the on-shell action at finite integer $M$ show that the nondiagonal replica-symme…

Analyticity of replica correlators and Modular ETH

We study the two point correlation function of a local operator on an $n$-sheeted replica manifold corresponding to the half-space in the vacuum state of a conformal field theory. In analogy with the inverse Laplace transform, we define the Renyi transform of this correlation function, which is a function of one complex variable $w$, dual to the Renyi parameter $n$. Inspired by the inversion formula of Caron-Huot, we argue that if the Renyi transform $f(w)$ has bounded behavior at infinity in the complex $w$ plane, the discontinuity of the Renyi transform disc $f(w)$ provides the unique analyt…

一维任意子气体的基态性质

Ground-state properties of one-dimensional anyon gases

基于任意耦合常数（$0\leq c\leq \infty$）和统计参数（$0\leq κ\leq π$）的Bethe精确解，研究了一维相互作用任意子系统的基态.结果表明，重整化耦合常数$c'$决定了准动量$k$空间的态密度和基态能量。统计参数$κ$对动量分布的影响表现在两个方面：除了重整化耦合的影响外，对于任意耦合常数$c$，当统计参数$κ$偏离0（玻色统计）和$π$（费米统计）时，非离子统计导致动量分布的非对称性.当$κ$从0变化到$π$时，动量分布从玻色分布演化到费米分布。非对称动量分布是由约化密度矩阵非对角元素虚部的贡献引起的，它是$κ$的奇函数。如果$κ$为负，则正动量处的峰将向负动量移动。