论文标题
$α$-Rényi熵的有限尺寸效果在扩张下脱节间隔
Scaling of finite size effect of $α$-Rényi entropy in disjointed intervals under dilation
论文作者
论文摘要
无间隙模型中的$α$-Rényi熵是通过保形场理论获得的，这在热力学极限中是准确的。但是，其有限尺寸效应（FSE）的计算具有挑战性。到目前为止，只有在XX模型中单个间隔的FSE已被理解，并且在其他模型中，在其他条件下的FSE完全未知。在这里，我们在XY模型中以均匀扩张$λa$下的脱节间隔报告了此熵的FSE $ a = \ cup_i a_i $ \ begin {equation*} Δ_{λa}^α=δ_a^αλ^{ - η} \ Mathcal {b}（a，λ）， \ end {equation*} 其中$ | \ Mathcal {b}（a，λ）| \ le 1 $是有界函数，$η= \ text {min}（2，2/α）$当$α<10 $。我们在XY模型的相边界中验证了这种关系，其中不同的中央电荷对应于自由费米和游离玻色子模型的物理。我们发现，在分离的间隔中，需要两个FSE，称为外部FSE和固有的FSE，才能充分说明熵的FSE。从物理上讲，我们发现仅在开放端$ \ partial a $的相关矩阵的边缘模式对总熵及其FSE有贡献。我们的结果为多体系统中的纠缠熵提供了一些敏锐的见解。
The $α$-Rényi entropy in the gapless models have been obtained by the conformal field theory, which is exact in the thermodynamic limit. However, the calculation of its finite size effect (FSE) is challenging. So far only the FSE in a single interval in the XX model has been understood and the FSE in the other models and in the other conditions are totally unknown. Here we report the FSE of this entropy in disjointed intervals $A = \cup_i A_i$ under a uniform dilation $λA$ in the XY model, showing of a universal scaling law as \begin{equation*} Δ_{λA}^α= Δ_A^αλ^{-η} \mathcal{B}(A, λ), \end{equation*} where $|\mathcal{B}(A, λ)| \le 1$ is a bounded function and $η= \text{min}(2, 2/α)$ when $α< 10$. We verify this relation in the phase boundaries of the XY model, in which the different central charges correspond to the physics of free Fermion and free Boson models. We find that in the disjointed intervals, two FSEs, termed as extrinsic FSE and intrinsic FSE, are required to fully account for the FSE of the entropy. Physically, we find that only the edge modes of the correlation matrix localized at the open ends $\partial A$ have contribution to the total entropy and its FSE. Our results provide some incisive insight into the entanglement entropy in the many-body systems.
