Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.
Physics Department, University of California, Davis, California 95616, USA.
Phys Rev Lett. 2013 Sep 6;111(10):107205. doi: 10.1103/PhysRevLett.111.107205. Epub 2013 Sep 5.
Topological phases are unique states of matter which support nonlocal excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement entropy (TEE). We study the finite size corrections to the TEE by focusing on systems with a Z2 topological ordered state using density-matrix renormalization group and perturbative series expansions. We find that extrapolations of the TEE based on the Renyi entropies with a Renyi index of n≥2 suffer from much larger finite size corrections than do extrapolations based on the von Neumann entropy. In particular, when the circumference of the cylinder is about ten times the correlation length, the TEE obtained using von Neumann entropy has an error of order 10(-3), while for Renyi entropies it can even exceed 40%. We discuss the relevance of these findings to previous and future searches for topological ordered phases, including quantum spin liquids.
拓扑相是物质的独特状态，支持非局域激发，其行为类似于具有分数统计的粒子。拓扑纠缠熵（TEE）为带隙拓扑相提供了通用的特征描述。我们通过使用密度矩阵重整化群和微扰级数展开来研究具有 Z2 拓扑有序态的系统中 TEE 的有限尺寸修正。我们发现，基于 Renyi 熵（Renyi index n≥2）的 TEE 外推比基于冯·诺依曼熵的外推受到更大的有限尺寸修正。特别是，当圆柱的周长大约是相关长度的十倍时，使用冯·诺依曼熵得到的 TEE 的误差约为 10(-3)，而对于 Renyi 熵，误差甚至可以超过 40%。我们讨论了这些发现与以前和未来对拓扑有序相的搜索的相关性，包括量子自旋液体。
