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，并在凝聚态物理学中得到广泛研究;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的狄拉克点为中心的相对论费米子，但带电自由度之间的相互作用的影响却不太清楚，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，因为通常没有允许受控近似的自然小参数，并且在泛函重整化群，共形引导和晶格模拟等工作者中，主要为粒子理论开发的工具，对于他们的从业者来说，这样的系统包含了他们各自议程的基本挑战。这个项目将建立在最近的工作基础上，发展格子场理论技术来模拟相互作用的平面系统与正确的整体对称性固有的相对论费米子，使用洞察力从域壁费米子制定最初开发的精确研究量子色动力学。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？是否有晶格公式在某种极限下产生预期的连续对称性？我们能把我们的方法从半填充扩展出去吗？什么是临界物种数低于量子临界点与动态能隙产生可以发生？相应的连续统量子场论的性质是什么？它的对称性是什么？是本地的吗？该项目将利用超级计算

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