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arXiv 1406.7477cond-mat.str-elcond-mat.stat-mech
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哈伯德模型的四分之一的纠缠熵

Entanglement Entropies of the quarter filled Hubbard model

Pasquale Calabrese, Fabian H. L. Essler, Andreas M. Lauchli

摘要:

研究了一维四分之一填充哈伯德模型在周期边界条件下基态的Renyi和von Neumann纠缠熵。我们发现,他们表现出意想不到的依赖系统的大小:对于L=4 mod 8的结果与预期的基础上共形场论,而L=0 mod 8的额外的贡献出现。我们表明,这些可以理解的“壳填充”的效果,我们开发了一个共形场论的方法来计算熵的额外贡献。这些分析结果与弱Hubbard相互作用下的密度矩阵重整化群计算结果非常吻合。我们认为,对于较大的相互作用的存在下,一个边际无关的运营商在自旋部门强烈影响的熵在有限的大小数值访问,我们提出了一个有效的方法来考虑到它们。

英文摘要:

We study Renyi and von Neumann entanglement entropies in the ground state of the one dimensional quarter-filled Hubbard model with periodic boundary conditions. We show that they exhibit an unexpected dependence on system size: for L=4 mod 8 the results are in agreement with expectations based on conformal field theory, while for L=0 mod 8 additional contributions arise. We show that these can be understood in terms of a "shell-filling" effect, and we develop a conformal field theory approach to calculate the additional contributions to the entropies. These analytic results are found to be in excellent agreement with density matrix renormalisation group computations for weak Hubbard interactions. We argue that for larger interactions the presence of a marginal irrelevant operator in the spin sector strongly affects the entropies at the finite sizes accessible numerically, and we present an effective way to take them into account.

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