Phase Diagram of Graphene from Lattice Field Theory

该项目利用石墨烯的电子特性与强耦合量子场理论之间的相似性，最重要的是量子色动力学（QCD），以解决与多体强耦合效应相关的一些突出问题，这些问题如今可以在高质量的石墨烯样品中进行越来越好的实验研究。基于我们最先进的晶格场理论工具的Ab-initio蒙特卡罗模拟用于系统地探索石墨烯在有利于各种有序相存在的外部影响下的相结构。石墨烯晶格上的Dyson-Schwinger方程补充了这些初始计算，例如，在非常大的体积或有限载流子密度下的伪共形行为，其中存在费米子符号问题，如在有限重子密度下的QCD。特别是，该项目旨在确定各种莫特绝缘相中哪些发生在可调参数的各个区域，以及它们是否可以通过实验实现。因此，它讨论了磁场和磁催化在重离子碰撞中的作用，作为预凝聚催化剂的缺陷及其与瞬子的类比，有限密度Lifshitz跃迁，以及热QCD中安德森局域化和手性对称性破缺之间的关系。目标是确定石墨烯如何最好地用于测试这种非微扰量子场论概念，这也与在良好可控实验条件下研究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.