标题： 标度对称性破缺与量子临界点处的质量产生 显示英文标题

标题： Scale symmetry breaking and generation of mass at quantum critical points

摘要： 我们研究了三维空间中由Yukawa相互作用和标量自相互作用耦合的$N$相对论狄拉克费米子与实标量场的渐近自由理论，使用的是泛函重正化方法。 在许多费米子味数极限下，由于量子涨落，三次标量耦合变得完全无关紧要，从而导致一条强耦合红外不动点线。 即使手征对称性不存在，费米子质量也可以通过量子相变生成。 不动点线由于真空稳定性丧失而在临界端点处终止。 正好在端点处，尺度对称性自发破缺，导致费米子质量的产生。 有趣的是，手征对称性的缺失是费米子质量自发生成的前提条件，而不是其结果。 我们还强调了Gross-Neveu和Gross-Neveu-Yukawa理论在临界点附近和远离临界点时的密切相似性，并确立了它们在大$N$极限下的泛函重正化群流和量子有效作用的大规模等价性。 进一步的含义包括对于共形场论的影响也有所指示。 显示英文摘要

摘要： We study an asymptotically free theory of $N$ relativistic Dirac fermions and a real scalar field coupled by Yukawa and scalar self-interactions in three dimensions using functional renormalisation. In the limit of many fermion flavours, the cubic scalar coupling becomes exactly marginal due to quantum fluctuations, leading to a line of strongly-coupled infrared fixed points. Fermion mass can be generated through a quantum phase transition even if chiral symmetry is absent. The line of fixed points terminates at a critical endpoint due to the loss of vacuum stability. Exactly at the endpoint, scale symmetry is broken spontaneously, leading to the generation of fermion mass. Intriguingly, the absence of chiral symmetry is a prerequisite for the spontaneous generation of fermion mass, and not a consequence thereof. We also highlight close similarities between Gross-Neveu and Gross-Neveu--Yukawa theories at and away from critical points, and establish the large-$N$ equivalence of their functional RG flows and quantum effective actions. Further implications including for conformal field theories are indicated.