Entanglement entropy of non-unitary conformal field theory
Entanglement entropy of non-unitary conformal field theory
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DOI：
10.1088/1751-8113/48/4/04ft01
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发表时间：
2015-01-30
影响因子：
2.1
通讯作者：
Ravanini, F.
中科院分区：
文献类型：
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作者：
Bianchini, D.;Castro-Alvaredo, O.;Ravanini, F.
本文证明了在基态破坏共形不变性的一维临界模型中，大尺寸l区域的Renyi纠缠熵（例如在由非幺正共形场论描述的那些场论中），表现为类似于c（eff）（n + 1）/6 n log 1的S-n，其中c（eff）= c - 24 Δ> 0是有效中心电荷，c（可以是负的）是共形场论的中心荷，而不等于0的Delta是该理论中的最低全纯共形维数。我们也得到了结果模型的边界，并与一个大的，但有限的相关长度，我们表明，如果最低的共形特征空间是对数（L-0 =三角洲I + N与N幂零），然后有一个额外的长期成比例的日志（日志l）。这些结果推广了酉模型的已知表达式。我们提供了一个一般的证明，并报告的数值证据的非酉自旋链和分析计算使用角转移矩阵方法的非酉晶格模型。我们使用一种新的代数技术来研究副本方法中出现的分支，并找到一个新的表达的纠缠熵的相关函数的扭曲领域的非酉模型。
Here we show that the Renyi entanglement entropy of a region of large size l in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as S-n similar to c(eff)(n + 1)/6n log l, where c(eff) = c - 24 Delta > 0 is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and Delta not equal 0 is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic (L-0 = Delta I + N with N nilpotent), then there is an additional term proportional to log (log l). These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models.