论文标题
Matrix产品状态的广泛的Rényi熵
Extensive Rényi entropies in matrix product states
论文作者
论文摘要
我们证明，通过通用（间隙）描述的旋转链的所有Rényi纠缠熵，转化不变的矩阵乘积状态（MPS）对于脱离的子系统而言：所有k-旋转型在每个k- senty inst intem inty ins of the noute in of intynem intynem inty and infodynem forty and infodynem inty and infodynem inthememif and infodynem infodynem in and of infodynem infodynem in and of infodynem infodynem的限制是否限制了A的热量，则该系统的范围限制是否为AN，如果是限制了A的限制。此外，我们根据MPS的转移操作员的扩展系数和其固定点的光谱特性以规范形式提供明确的下限，以纠缠熵。作为侧向重点，我们根据其定点的kraus级和熵特性，获得了一个原始量子通道的膨胀系数和奇异值分布的下限。对于Unital量子通道，这会产生非常简单的下限，这是对单数值的分布和Kraus级别的膨胀系数。从物理上讲，我们的结果是由关于多体局部系统平衡的问题所激发的，我们会审查。
We prove that all Rényi entanglement entropies of spin-chains described by generic (gapped), translational invariant matrix product states (MPS) are extensive for disconnected sub-systems: All Rényi entanglement entropy densities of the sub-system consisting of every k-th spin are non-zero in the thermodynamic limit if and only if the state does not converge to a product state in the thermodynamic limit. Furthermore, we provide explicit lower bounds to the entanglement entropy in terms of the expansion coefficient of the transfer operator of the MPS and spectral properties of its fixed point in canonical form. As side-result we obtain a lower bound for the expansion coefficient and singular value distribution of a primitve quantum channel in terms of its Kraus-rank and entropic properties of its fixed-point. For unital quantum channels this yields a very simple lower bound on the distribution of singular values and the expansion coefficient in terms of the Kraus-rank. Physically, our results are motivated by questions about equilibration in many-body localized systems, which we review.
