AI 中文总结
研究二维狄拉克半金属在量子临界点附近情况，用非微扰场论方法研究手征伊辛模型相图，确定零温量子临界点及性质、有限温度相变，还明确了量子临界扇范围等，提供了统一场论框架。
AI 中文摘要
量子临界点附近的二维狄拉克半金属可用格罗斯 - 内夫 - 汤川模型描述。鉴于近期在高度可调的范德瓦尔斯异质结构中展现出从狄拉克半金属到绝缘体的转变这一实验进展，更好地理解有限温度效应很有必要。本文用非微扰场论方法研究了手征伊辛模型在零温和有限温度下，半金属相和具有自发破缺\(\mathbb{Z}_2\)对称性的绝缘相中的格罗斯 - 内夫 - 汤川相图。零温时发现一个量子临界点，其临界指数接近手征伊辛普适类，且在量子临界点附近涌现出相对论对称性。有限温度下，有序相存在到有限临界温度，此时发生向无序相的经典相变，此相变属于二维伊辛普适类。最后确定了量子临界扇的范围和标度性质以及其中的准粒子权重行为。总之，为手征伊辛模型在其量子临界点周围的相图提供了一个统一的场论框架。
英文摘要
Two-dimensional Dirac semimetals near a quantum critical point can be described by Gross--Neveu--Yukawa models. In view of recent experimental advances exhibiting a transition from Dirac semimetal to insulator in highly-tunable van-der-Waals heterostructures, a better understanding of finite-temperature effects is mandatory. Here, we study the Gross--Neveu--Yukawa phase diagram of the chiral Ising model with a non-perturbative field-theory approach at zero and finite temperature, both in the semimetallic phase and in the insulating phase with spontaneously broken $\mathbb{Z}_2$ symmetry. At zero temperature, we find a quantum critical point with critical exponents that are close to the ones of the chiral Ising universality class, and show that relativistic symmetry is emergent close to the quantum critical point. At finite temperature, the ordered phase survives up to a finite critical temperature, at which we observe a classical phase transition into the disordered phase. We confirm that this transition lies in the two-dimensional Ising universality class. Finally, we determine the extent and scaling properties of the quantum critical fan, and the behavior of the quasiparticle weight, therein. In summary, we present a unified field-theoretical framework for the phase diagram of the chiral Ising model in the surroundings of its quantum critical point.
Comments11+12 pages, 7+3 figures
