AI 中文总结
研究二维极化费米气体的FFLO相变，提出自洽扩展方法得到一致相图，揭示其量子临界行为，对比二维与三维系统，证明三维FFLO相变属平均场普适类。
AI 中文摘要
我们利用图解t矩阵方法，研究二维费米气体在零温下从极化正常相到FFLO态的相变。首先，我们发现标准非自洽理论因严重违反卢瑟福定理，会产生非物理的相图。基于该观察，我们引入一种最小自洽扩展，其在保留原有形式体系分析简洁性的同时，大幅恢复了对卢瑟福定理的遵从性，这使得在整个相互作用范围内得到了物理上一致的相图。基于该改进描述，我们通过准粒子衰减率、准粒子权重、动量分布以及费米和玻色自由度的临界动力学，表征了FFLO相变的量子临界行为。我们进一步对比了二维和三维系统，表明它们的临界性质可通过基于多数和少数费米面嵌套的统一几何图像来理解。最后，对于三维情况，我们在赫茨-米利斯框架内证明顶点修正是无关的，从而将FFLO量子相变归入平均场普适类，与巡游反铁磁体高度类似。
英文摘要
We investigate the zero-temperature transition from the polarized normal phase to the FFLO state in a two-dimensional Fermi gas by means of a diagrammatic t-matrix approach. We first show that the standard non-self-consistent theory produces an unphysical phase diagram because of a severe violation of the Luttinger theorem. Motivated by this observation, we introduce a minimal self- consistent extension that largely restores compliance with the Luttinger theorem while preserving the analytical simplicity of the original formalism. This leads to a physically consistent phase diagram over the whole interaction range. Building on this improved description, we characterize the quantum critical behavior of the FFLO transition through the quasiparticle decay rates, quasiparticle weights, momentum distributions, and the critical dynamics of both fermionic and bosonic degrees of freedom. We further compare the two- and three-dimensional systems, showing that their critical properties can be understood within a unified geometrical picture based on the nesting of the majority and minority Fermi surfaces. Finally, for the three-dimensional case, we demonstrate within the Hertz-Millis framework that vertex corrections are irrelevant, thereby placing the FFLO quantum phase transition in the mean-field universality class, in close analogy with itinerant antiferromagnets.
Comments32 pages, 17 figures
