标题： 比热和密度在哈伯德模型中的异常现象 显示英文标题

标题： Specific heat and density anomalies in the Hubbard model

摘要： 理解材料的热学性质对于技术应用和发现新现象是基础性的。特别是实验技术的进步，如冷原子测量，使得能够以对模型参数（如费米-哈伯德模型）的高度控制来模拟典型的哈密顿量。这个模型的一个方面尚未被广泛探索，即比热容随密度的变化行为。在本工作中，我们对哈伯德模型进行了行列式量子蒙特卡洛模拟，以分析当系统的填充、相互作用和温度变化时的比热容。我们发现，在强关联情况下，比热容随填充变化呈现三峰结构，在它们之间有局部极小值。这种效应可以通过比热容的动能和势能贡献的分解来解释。此外，通过分析动量空间中的动能贡献，我们表明，与这种比热容行为相关，通过热膨胀系数检测到一个密度异常。这些动量空间量可以通过冷原子实验获得。最后，我们将这些现象的位置进行映射，并将热膨胀异常与众所周知的塞贝克系数符号变化联系起来。我们的结果提供了一种新的视角来分析这种符号变化。此外，我们的比热容结果展示了远离通常研究的半填充区域的有趣现象。 显示英文摘要

摘要： Understanding thermal properties of materials is fundamental to technological applications and to discover new phenomena. In particular, advances of experimental techniques such as cold-atoms measurements allow the simulation of paradigmatic Hamiltonians with great control over model parameters, such as the Fermi-Hubbard model. One aspect of this model which is not much explored is the behavior of the specific heat as function of density. In this work, we perform Determinant Quantum Monte Carlo simulations of the Hubbard model to analyze the specific heat as the filling, interaction and temperature of the system is changed. We found that, with strong correlations, the specific heat presents a three-maxima structure as a function of filling, with local minima between them. This effect can be explained by a decomposition of kinetic and potential contributions to the specific heat. Moreover, by analyzing the kinetic contribution in momentum space we show that, connected to this specific heat behavior, there is a density anomaly detected through the thermal expansion coefficient. These momentum-space quantities are accessible using cold-atoms experiments. Finally, we map the location of these phenomena and connect the thermal expansion anomaly with the well-known Seebeck coefficient change of sign. Our results provide a new perspective to analyze this change of sign. Moreover, our specific heat results demonstrate interesting phenomena away from the commonly studied half-filling regime.