Entanglement entropy after a partial projective measurement in 1 + 1 dimensional conformal field theories: exact results
Entanglement entropy after a partial projective measurement in 1 + 1 dimensional conformal field theories: exact results
复制标题
1 + 1 维共形场论中部分投影测量后的纠缠熵：精确结果
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
M. Rajabpour
中科院分区：
文献类型：
--
作者：
M. Rajabpour
在对系统的一部分进行投影测量后，我们解析地计算了1 + 1维共形场理论（CFT）基态的r<s:1>二部纠缠熵Sα。我们证明了这种设置中的纠缠熵依赖于系统的中心电荷和算子的内容。当测量区域A将两个部分B和B¯分开时，B和B¯之间的纠缠熵相对于两个区域之间的特征距离像幂律一样减少，其指数依赖于r<s:1>纠缠熵的秩α和系统中存在的最小标度维。在确定了一些振子的位置（部分测量）后，我们通过对Klein-Gordon场理论（耦合谐振子）进行数值计算来验证我们的发现。我们还对大质量量子场理论中的测量后纠缠熵进行了评述。
We calculate analytically the Rényi bipartite entanglement entropy Sα of the ground state of 1 + 1 dimensional conformal field theories (CFT) after performing a projective measurement in part of the system. We show that the entanglement entropy in this setup is dependent on the central charge and the operator content of the system. When the measurement region A separates the two parts B and B¯, the entanglement entropy between B and B¯ decreases like a power-law with respect to the characteristic distance between the two regions with an exponent which is dependent on the rank α of the Rényi entanglement entropy and the smallest scaling dimension present in the system. We check our findings by making numerical calculations on the Klein–Gordon field theory (coupled harmonic oscillators) after fixing the position (partial measurement) of some of the oscillators. We also comment on the post-measurement entanglement entropy in the massive quantum field theories.