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arXiv 2406.12967cond-mat.str-elhep-th
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临界费米面的涨落谱

Fluctuation Spectrum of Critical Fermi Surfaces

Cornell University(康奈尔大学)

Haoyu Guo

AI总结:

研究临界费米面与伊辛-凝胶量子临界点耦合的涨落谱,揭示软模式动力学及非费米液体输运特性。

摘要:

我们研究了一个费米面与伊辛-凝胶量子临界点在(2+1)时空中维数耦合的低能有效理论。我们利用大N的Yukawa-SYK模型来描述该系统,其极点由Migdal-Eliashberg方程描述。通过研究极点周围的高斯涨落谱,可以揭示低能物理,该谱由Bethe-Salpeter核K_BS生成。基于守恒恒等式,我们提出一个在两个点函数空间上的内积,揭示了K_BS的大量软模式。这些软模式参数化费米面的变形,其涨落本征值描述其衰减率。我们对圆形费米面计算这些本征值,并发现奇宇称模式比偶宇称模式具有参数级更长的寿命,这是由于费米子在凸费米面散射的动力学约束。本征值的符号信号在零温度下对于凸费米面的伊辛-凝胶量子临界点的不稳定性。在有限温度下,系统可以通过临界玻色子的热涨落稳定。我们推导了一个描述软模式动力学的有效作用量,它导致一个线性化的玻尔兹曼方程,其中本征值的实部可以解释为碰撞率。有效作用量的结构类似于费米面的线性玻色化理论。作为应用,我们研究了非费米液体的流体输运。分析玻尔兹曼方程,我们得到常规流体输运 regime 和图谱输运 regime。在两种 regime 中,系统在有限几何中的导电性可以是软模式动力学和非费米液体物理的尖锐指示器。

英文摘要:

We investigate the low-energy effective theory of a Fermi surface coupled to an Ising-nematic quantum critical point in (2+1) spacetime dimensions with translation symmetry. We formulate the system using the large $N$ Yukawa-SYK model, whose saddle point is described by the Migdal-Eliashberg equations. The low-energy physics can be revealed by studying the Gaussian fluctuation spectrum around the saddle point, which is generated by the Bethe-Salpeter kernel $K_\text{BS}$. Based on the Ward identities, we propose an inner product on the space of two point functions, which reveals a large number of soft modes of $K_\text{BS}$. These soft modes parameterize deformation of the Fermi surface, and their fluctuation eigenvalues describe their decay rates. We analytically compute these eigenvalues for a circular Fermi surface, and we discover the odd-parity modes to be parametrically longer-lived than the even-parity modes, due to the kinematic constraint of fermions scattering on a convex FS. The sign of the eigenvalues signals an instability of the Ising-nematic quantum critical point at zero temperature for a convex Fermi surface. At finite temperature, the system can be stabilized by thermal fluctuations of the critical boson. We derive an effective action that describes the soft-mode dynamics, and it leads to a linearized Boltzmann equation, where the real part of the soft-mode eigenvalues can be interpreted as the collision rates. The structure of the effective action is similar to the theory of linear bosonization of a Fermi surface. As an application, we investigate the hydrodynamic transport of non-Fermi liquid. Analyzing the Boltzmann equation, we obtain a conventional hydrodynamic transport regime and a tomographic transport regime. In both regimes, the conductance of the system in finite geometry can be a sharp indicator for the soft-mode dynamics and non-Fermi liquid physics.

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