Phase Diagram of Graphene from Lattice Field Theory

这个项目利用石墨烯的电子性质和强耦合量子场理论之间的类比，最重要的是量子色动力学(QCD)，来解决与多体强耦合效应有关的一些悬而未决的问题，这些效应现在可以越来越好地在高质量的石墨烯样品中进行实验研究。基于我们最先进的晶格场理论工具，采用从头算蒙特卡罗模拟方法系统地研究了石墨烯在外界影响下的相结构，这些影响有利于各种有序相的存在。石墨烯晶格上的Dyson-Schwinger方程补充了这些从头计算，例如，对于非常大的体积中的伪共形行为或有限的电荷载流子密度，其中存在费米子符号问题，就像在有限重子密度的QCD中一样。特别是，该项目的目的是确定各种Mott绝缘相中的哪些出现在可调参数的不同区域，以及它们是否可以在实验上实现。因此，它解决了重离子碰撞中的磁场和磁催化，预缩合催化剂的缺陷及其与瞬子的类比，有限密度Lifshitz跃迁，以及Anderson局域化和手性对称破缺之间的关系，如在热QCD中。我们的目标是确定如何最好地使用石墨烯来测试这样的非微扰量子场论概念，这些概念也与在良好可控的实验条件下研究QCD相图有关。

This project exploits analogies between the electronic properties of graphene and strongly coupled quantum field theories, most importantly quantum chromodynamics (QCD), to address some of the outstanding questions in relation to many-body strong-coupling effects which can nowadays increasingly well be studied experimentally in high quality samples of graphene. Ab-initio Monte-Carlo simulations based on our state-of-the-art tools from lattice field theory are used tosystematically explore the phase structure of graphene in the presence of external influences which favor various ordered phases. Dyson-Schwinger equations on the graphene lattice complement these ab-initio calculations, e.g., for pseudo-conformal behavior in very large volumes or finite charge-carrier densities where there is a fermion-sign problem as in QCD at finite baryon density. In particular, the project aims to determine which of the various Mott insulating phases occur inthe various regions of tunable parameters and whether they can be realized experimentally. It thereby addresses magnetic fields and magnetic catalysis as also relevant in heavy-ion collisions, defects as catalysts for pre-condensation and their analogies with instantons, the finite-density Lifshitz transition, and the relation between Anderson localization and chiral symmetry breaking as in hot QCD. The goal is to identify how graphene can best be used to test such non-perturbative quantum field theory concepts as also relevant for studies of the QCD phase diagram under well controllable experimental conditions.