论文标题
量子晶状膜的扰动重新归一化和热力学
Perturbative renormalization and thermodynamics of quantum crystalline membranes
论文作者
论文摘要
我们分析了系统扰动重新归一化组（RG）框架内独立量子晶体膜的统计力学。功率计数分析表明，可以在有效的可重新分析模型中分析相关函数的主要奇异性，在该模型中，在菌株张量扩展中，平面声子的动能和二级几何非线性被忽略。对于由零点运动控制的零温度下的膜，有效模型的RG方程将对数校正对弯曲刚度和早期研究中衍生的弹性幼年模量提供了系统的推导。在弱应用的外部张力的限制下，应力 - 应变关系在$ t = 0 $是异常的：线性胡克定律被奇异的法律所取代，该法律显示出对数校正的奇异定律。 For small, but finite temperatures, we use techniques of finite-size scaling to derive general relations between the zero-temperature RG flow and scaling laws of thermodynamic quantities such as the thermal expansion coefficient $α$, the entropy S, and the specific heat C. A combination of the scaling relations with an analysis of thermal fluctuations shows that, for small temperatures, the thermal expansion coefficient $α$ is negative and正如早期工作所预测的那样，对数取决于$ t $。尽管要求$ \ lim_ {t \ to 0}α= 0 $，但预期的是，从热力学的第三定律中预期，$α$的预计会表现出如此缓慢的变化，以保持几乎恒定的恒定至不可接受的小温度。
We analyze the statistical mechanics of a free-standing quantum crystalline membrane within the framework of a systematic perturbative renormalization group (RG). A power-counting analysis shows that the leading singularities of correlation functions can be analyzed within an effective renormalizable model in which the kinetic energy of in-plane phonons and subleading geometrical nonlinearities in the expansion of the strain tensor are neglected. For membranes at zero temperature, governed by zero-point motion, the RG equations of the effective model provide a systematic derivation of logarithmic corrections to the bending rigidity and to the elastic Young modulus derived in earlier investigations. In the limit of a weakly applied external tension, the stress-strain relation at $T = 0$ is anomalous: the linear Hooke's law is replaced with a singular law exhibiting logarithmic corrections. For small, but finite temperatures, we use techniques of finite-size scaling to derive general relations between the zero-temperature RG flow and scaling laws of thermodynamic quantities such as the thermal expansion coefficient $α$, the entropy S, and the specific heat C. A combination of the scaling relations with an analysis of thermal fluctuations shows that, for small temperatures, the thermal expansion coefficient $α$ is negative and logarithmically dependent on $T$, as predicted in an earlier work. Although the requirement $\lim_{T \to 0} α= 0$, expected from the third law of thermodynamics is formally satisfied, $α$ is predicted to exhibit such a slow variation to remain practically constant down to unaccessibly small temperatures.
