arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1807.10409cond-mat.str-elcond-mat.quant-gasquant-ph
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二维哈伯德模型中Mott相变的热力学和信息论描述

Thermodynamic and information-theoretic description of the Mott transition in the two-dimensional Hubbard model

C. Walsh, P. Sémon, D. Poulin, G. Sordi, A. -M. S. Tremblay

摘要:

在莫特转变时,电子-电子相互作用将电子在其中流动的金属改变为电子在其中局域化的绝缘体。这种现象是量子材料的核心。本文利用元胞动力学平均场论研究了有限温度下的二维哈伯德模型。我们提供了一个详尽的热力学描述的相关驱动的Mott转变的半充满模型通过计算压力,电荷压缩性,熵,动能,势能和自由能跨越一阶Mott转变和高温交叉(Widom线)。熵提取的吉布斯-迪昂关系,并显示出复杂的行为附近的过渡,标记为不连续的跳跃在一阶边界,奇异行为在莫特端点和拐点标记急剧变化的超临界区域。自由能使我们能够确定热力学相边界,讨论相稳定性和亚稳性,并触及成核和旋节分解机制的过渡。我们补充这一热力学描述的莫特过渡的信息理论的描述。我们通过计算局域熵和单点总互信息来实现这一点,局域熵是纠缠的一种度量,单点总互信息量化了量子和经典关联。这些信息理论的措施表现出的特征行为,使我们能够确定的一阶共存区域,莫特临界端点和跨沿Widom线在超临界区域。

英文摘要:

At the Mott transition, electron-electron interaction changes a metal, in which electrons are itinerant, to an insulator, in which electrons are localized. This phenomenon is central to quantum materials. Here we contribute to its understanding by studying the two-dimensional Hubbard model at finite temperature with plaquette cellular dynamical mean-field theory. We provide an exhaustive thermodynamic description of the correlation-driven Mott transition of the half-filled model by calculating pressure, charge compressibility, entropy, kinetic energy, potential energy and free energy across the first-order Mott transition and its high-temperature crossover (Widom line). The entropy is extracted from the Gibbs-Duhem relation and shows complex behavior near the transition, marked by discontinuous jumps at the first-order boundary, singular behavior at the Mott endpoint and inflections marking sharp variations in the supercritical region. The free energy allows us to identify the thermodynamic phase boundary, to discuss phases stability and metastability, and to touch upon nucleation and spinodal decomposition mechanisms for the transition. We complement this thermodynamic description of the Mott transition by an information-theoretic description. We achieve this by calculating the local entropy, which is a measure of entanglement, and the single-site total mutual information, which quantifies quantum and classical correlations. These information-theoretic measures exhibit characteristic behaviors that allow us to identify the first-order coexistence regions, the Mott critical endpoint and the crossovers along the Widom line in the supercritical region.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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