Entropy and modular Hamiltonian for a free chiral scalar in two intervals
Entropy and modular Hamiltonian for a free chiral scalar in two intervals
复制标题
两个区间内自由手性标量的熵和模哈密顿量
作者：
Raúl Arias;H. Casini;M. Huerta;D. Pontello
本文计算了两个区间区域的真空模哈密顿量的解析形式，以及d=2$中的手征自由标量φ $对应的电流$j（x）=部分φ（x）$的代数。我们还明确计算区间之间的互信息。这个模型显示了一个失败的哈格对偶的两个间隔，转换成一个损失的对称性的互信息通常与模不变性。与自由无质量费米子的情况相反，模哈密顿量是完全非定域的。通过计算相关器核算子的本征系统来对角化密度矩阵来完成计算。这些特征向量是通过一种新的方法，涉及解决一个等价的问题，在复平面上的乘法边界条件施加在区间上的全纯函数。使用同样的技术，我们也重新推导出自由费米子模哈密顿量在一个更透明的方式。
We calculate the analytic form of the vacuum modular Hamiltonian for a two interval region and the algebra of a current $j(x)=partial phi(x)$ corresponding to a chiral free scalar $phi$ in $d=2$. We also compute explicitly the mutual information between the intervals. This model shows a failure of Haag duality for two intervals that translates into a loss of a symmetry property for the mutual information usually associated with modular invariance. Contrary to the case of a free massless fermion, the modular Hamiltonian turns out to be completely non local. The calculation is done diagonalizing the density matrix by computing the eigensystem of a correlator kernel operator. These eigenvectors are obtained by a novel method that involves solving an equivalent problem for an holomorphic function in the complex plane where multiplicative boundary conditions are imposed on the intervals. Using the same technique we also re-derive the free fermion modular Hamiltonian in a more transparent way.
CFT 中的相对熵
影响因子：
1.7
作者：
Longo, Roberto;Xu, Feng
通讯作者：
Xu, Feng