Finite-size corrections of the Entanglement Entropy of critical quantum chains
Finite-size corrections of the Entanglement Entropy of critical quantum chains
复制标题
临界量子链纠缠熵的有限尺寸修正
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
F. C. Alcaraz
中科院分区：
文献类型：
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作者：
J. Xavier;F. C. Alcaraz
利用密度矩阵重整化群计算了几个临界量子链的纠缠α-Renyi熵的有限尺寸修正。我们考虑了具有U（1）对称性的模型，如自旋为1/2的XXZ和自旋为1的Fateev-Zamolodchikov模型，以及具有离散对称性的模型，如Ising，Blume-Capel和三态Potts模型。这些更正包含物理相关信息。它们的振幅取决于α的值，与控制临界量子链长距离关联的共形场论中算子的维数有关。所得到的结果与以前的精确和数值的，使我们能够制定一些一般的approaches负责领先的有限尺寸校正的$alpha$-Renyi熵的运营商。我们推测，当α>1时，α-Renyi熵的前导有限尺寸修正的指数为p_{α}=2X_{1}/α，当p_{1}=2X_{2}/α时，α-Renyi熵的前导有限尺寸修正的指数为2X_{2}/α。
u$，其中$X_{x}$是模型能量算子的维数，$
对于所有模型，u=2$。
Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement $alpha$-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry like the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well models with discrete symmetries such as the Ising, the Blume-Capel and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, that depend on the value of $alpha$, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the $alpha$-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the $alpha$-Renyi entropies is $p_{alpha}=2X_{epsilon}/alpha$ for $alpha>1$ and $p_{1}=
u$, where $X_{epsilon}$ is the dimensions of the energy operator of the model and $
u=2$ for all the models.