一维无限格点系统块-块互信息的临界指数
Critical exponents of block-block mutual information in one-dimensional infinite lattice systems
摘要：
利用冯诺伊曼熵研究了一维无限格点系统中两个格块之间的互信息。用无限矩阵乘积态（iMPS）方法数值研究了量子$q$态Potts模型和横场自旋- $1/2$ XY模型.当系统参数变化时，块-块互信息表现出奇异行为，这使得能够识别量子相变的临界点。正如单个块的冯诺依曼纠缠熵所发生的那样，在临界点处，在$2\ell$连续位点的晶格块中均匀划分的两个$\ell$连续位点的晶格块之间的块-块互信息表现出对数领先行为，这产生了基础共形场论的中心荷$c$。随着两个格块之间的距离的增加，互信息揭示了一个一致的幂律衰减行为的截断维数和格块大小。在有限截断维数下，通过外推幂律衰减区域的指数，估计了热力学极限下块-块互信息的临界指数。对于给定的格块大小$\ell$，相同普适类的临界指数似乎彼此具有非常接近的值。不同普适性类的临界指数值不同，有一定的区别。随着格块尺寸的增大，临界指数减小。
英文摘要：
We study the mutual information between two lattice-blocks in terms of von Neumann entropies for one-dimensional infinite lattice systems. Quantum $q$-state Potts model and transverse field spin-$1/2$ XY model are considered numerically by using the infinite matrix product state (iMPS) approach. As a system parameter varies, block-block mutual informations exhibit a singular behavior that enables to identify critical points for quantum phase transition. As happens with the von Neumann entanglement entropy of a single block, at the critical points, the block-block mutual information between the two lattice-blocks of $\ell$ contiguous sites equally partitioned in a lattice-block of $2\ell$ contiguous sites shows a logarithmic leading behavior, which yields the central charge $c$ of the underlying conformal field theory. As the separation between the two lattice-blocks increases, the mutual information reveals a consistent power-law decaying behavior for various truncation dimensions and lattice-block sizes. The critical exponent of block-block mutual information in the thermodynamic limit is estimated by extrapolating the exponents of power-law decaying regions for finite truncation dimensions. For a given lattice-block size $\ell$, the critical exponents for the same universality classes seem to have very close values each other. Whereas the critical exponents have different values to a degree of distinction for different universality classes. As the lattice-block size becomes bigger, the critical exponent becomes smaller.
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