标题： 费米面作为量子临界流形：零能隙、序参量和$d$维度中的标度 显示英文标题

标题： Fermi surface as a quantum critical manifold: gaplessness, order parameter, and scaling in $d$-dimensions

摘要： 我们研究了几种$d$维费米子（$d=1,2,3$）的模型，重点在于它们无能隙（金属态）相的特性。 它在$T = 0$处作为连续相变发生，当配分函数的零点达到参数的真实范围时。 这些零点定义了$(d-1)$流形的量子临界性（费米面）。 它的出现或重构对应于利夫希茨转变。 这种$(d-1)$膜破坏了动量空间的对称性，导致无能隙激发，这是金属相的特征。 为了定量探测无能隙相，我们引入了几何序参数，即$d$的费米海体积。 通过对链、梯子和不同谱的自由费米子进行分析，这一提议被证明与其他量在利夫希茨点附近的标度一致：相关长度、振荡波长、磁化率和纠缠。 所有的（超）标度关系都得到了满足。 两个相互作用的汤川-卢廷格（$d=1$）和费米（$d=2,3$）液体的情况被分析，得出与自由费米子相同的普适性类。 显示英文摘要

摘要： We study several models of $d$-dimensional fermions ($d=1,2,3$) with an emphasis on the properties of their gapless (metallic) phase. It occurs at $T = 0$ as a continuous transition when zeros of the partition function reach the real range of parameters. Those zeros define the $(d-1)$-manifold of quantum criticality (Fermi surface). Its appearance or restructuring correspond to the Lifshitz transition. Such $(d-1)$-membrane breaks the symmetry of the momentum space, leading to gapless excitations, a hallmark of metallic phase. To probe quantitatively the gapless phase we introduce the geometric order parameter as $d$-volume of the Fermi sea. From analysis of the chain, ladder, and free fermions with different spectra, this proposal is shown to be consistent with scaling near the Lifshitz points of other quantities: correlation length, oscillation wavelength, susceptibilities, and entanglement. All the (hyper)scaling relations are satisfied. Two interacting cases of the Tomonaga-Luttinger ($d=1$) and the Fermi ($d=2,3$) liquids are analysed, yielding the same universality classes as free fermions.