Aspects of Strongly-Inetracting Quantum Fiueld Theory in Three Spacetime Dimensions

平面费米子经常出现在层状系统中，并在凝聚态物理中得到了广泛的研究；例如，石墨烯的电子性质长期以来一直被理解为以动量空间中狄拉克点为中心的相对论费米子，但携带电荷的自由度之间的相互作用对其影响的了解较少，仍然是一个活跃的研究领域。2+1D中的量子费米子也提出了许多理论挑战，因为通常不存在允许受控近似的自然小参数，而且人们对功能重整化群、共形自举和晶格模拟等领域的工作兴趣的复兴，这些工具主要是为粒子理论开发的，对于从业者来说，这样的系统概括了他们各自议程的基本挑战。这个项目将建立在最近开发的格点场理论技术的基础上，利用最初为量子色动力学中的精确研究而开发的域壁费米子公式，来模拟具有相对论费米子固有的正确全局对称性的相互作用的平面系统。需要解决的问题：我们如何控制强相互作用动力学的计算，并有信心将其应用于现实的凝聚态问题？有没有在一定限度内产生预期连续体对称性的晶格公式？我们能不能将我们的方法从半填充法扩展到另一种呢？低于这个临界点的量子临界点与动态能隙的产生有关？相应的连续统量子场论的本质是什么？它的对称性是什么？是本地的吗？该项目将利用这两个超级计算

Planar fermions occur frequently in layered systems and are extensively studied in condensed matter physics; for instance, electronic properties of graphene have long been understood in terms of relativistic fermions centred on Dirac points in momentum space, but the influence of interactions between charge-carrying degrees of freedom is less well-understood and remains an active field of study. Quantum fermions in 2+1d also present many theoretical challenges, since there is often no natural small parameter permitting a controlled approximation, and there is a renaissance of interest involving among others workers in functional renormalisation group, conformal bootstrap, and lattice simulation, tools mainly developed for particle theory, for whose practitioners such systems encapsulate essential challenges for their respective agendas.This project will build on recent work developing lattice field theory techniques for simulating interacting planar systems with the correct global symmetries intrinsic to relativistic fermions, using insight from the Domain Wall Fermion formulation originally developed for precision studies in Quantum Chromodynamics. Issues to be addressed:How can we control the calculation of strongly-interacting dynamics, and have confidence to apply it to realistic condensed matter problems? Are there lattice formulations yielding the expected continuum symmetries in some limit? Can we extend our methods away from half-filling?What is the critical number of species below which quantum critical points associated with dynamical gap generation can occur? What is the nature of the corresponding continuum quantum field theory? What are its symmetries? Is it local?The project will exploit both Supercomputing