随机质量Dirac费米子的重整化群分析
Renormalization group analysis of Dirac fermions with random mass
摘要：
二维D类无序超导体（SC）在扩散热金属（DTM）、拓扑超导体（TS）和常规局域（AI）相之间表现出无序诱导的量子多临界现象。为了刻画这三个相相遇的量子三临界点，我们对具有随机质量的二维Dirac费米子在空间维度$d=2-ε$上的$ε$展开进行了双圈重整化群（RG）分析.在二维（$ε=0$）中，无带隙狄拉克费米子的一个干净极限不动点附近，随机质量几乎不相关，而在有限无序强度下，存在一个对应于三临界点的IR不稳定不动点.的临界指数，动力学指数，和标度维数的（均匀）质量项的评估周围的三临界点的双环RG分析。利用二维无规质量Dirac费米子有效理论与（1+1）维Gross-Neveu模型之间的映射，我们进一步推导了临界指数的四圈计算，以及三临界点附近均匀质量的标度维数.两回线和四回线的计算结果都表明，在有限均匀质量下，AI-DTM转捩线和TS-DTM转捩线的临界性都受其它鞍点不动点的控制。
英文摘要：
Two-dimensional (2D) disordered superconductor (SC) in class D exhibits a disorder-induced quantum multicritical phenomenon among diffusive thermal metal (DTM), topological superconductor (TS), and conventional localized (AI) phases. To characterize the quantum tricritical point where these three phases meet, we carry out a two-loop renormalization group (RG) analysis for 2D Dirac fermion with random mass in terms of the $ε$-expansion in the spatial dimension $d=2-ε$. In 2D ($ε=0$), the random mass is marginally irrelevant around a clean-limit fixed point of the gapless Dirac fermion, while there exists an IR unstable fixed point at finite disorder strength that corresponds to the tricritical point. The critical exponent, dynamical exponent, and scaling dimension of the (uniform) mass term are evaluated around the tricritical point by the two-loop RG analysis. Using a mapping between an effective theory for the 2D random-mass Dirac fermion and the (1+1)-dimensional Gross-Neveu model, we further deduce the four-loop evaluation of the critical exponent, and the scaling dimension of the uniform mass around the tricritical point. Both the two-loop and four-loop results suggest that criticalities of a AI-DTM transition line as well as TS-DTM transition line are controlled by other saddle-point fixed point(s) at finite uniform mass.
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