论文标题
关键二次费米子的通用系统中的Rényi（香农）熵的通用对数校正
Universal logarithmic correction to Rényi (Shannon) entropy in generic systems of critical quadratic fermions
论文作者
论文摘要
rényi（香农）熵，即当地基地中量子系统的基态状态的$re_α（sh）$，通常显示体积法律行为。对于临界点处的量子链子系统，有一个额外的对数超脱头术语，其系数是通用的。在本文中，我们研究了该系数，用于通用时间反转翻译不变的二次临界免费费米。这些模型可以通过在单位圆上具有零的复杂函数进行参数化。当单元圆上的零没有退化，并且在单位圆外没有零，我们就可以对对数的系数进行分类。特别是，我们以数值方式计算出rényi（香农）的熵，用于各种模型，并表明有两个不同的类别。对于具有$ u（1）$对称的系统，系数与中心电荷成正比，即可以线性化系统的分散关系的点数的一半；对于$α$的所有值，其过渡点为$α= 4 $。对于没有这种对称性的系统，当$α> 1 $时，此系数再次与中心电荷成正比。但是，$α\ leq 1 $的系数是一个新的通用数字。最后，通过使用ISING链的Bisognano-Wichmann模块化哈密顿量的离散版本，我们表明这些系数是通用的，并且取决于基础CFT。
The Rényi (Shannon) entropy, i.e. $Re_α(Sh)$, of the ground state of quantum systems in local bases normally show a volume-law behavior. For a subsystem of quantum chains at critical point there is an extra logarithmic subleading term with a coefficient which is universal. In this paper we study this coefficient for generic time-reversal translational invariant quadratic critical free fermions. These models can be parameterized by a complex function which has zeros on the unit circle. When the zeros on the unit circle do not have degeneracy and there is no zero outside of the unit circle we are able to classify the coefficient of the logarithm. In particular, we numerically calculate the Rényi (Shannon) entropy in configuration basis for wide variety of these models and show that there are two distinct classes. For systems with $U(1)$ symmetry the coefficient is proportional to the central charge, i.e. one half of the number of points that one can linearize the dispersion relation of the system; for all the values of $α$ with transition point at $α=4$. For systems without this symmetry, when $α>1$ this coefficient is again proportional to the central charge. However, the coefficient for $α\leq 1$ is a new universal number. Finally, by using the discrete version of Bisognano-Wichmann modular Hamiltonian of the Ising chain we show that these coefficients are universal and dependent on the underlying CFT.
