Intertwined orders and exotic phase transitions in Dirac fermions

互操作命令可以相互竞争或兼容。当从狄拉克费米子的观点来理解时，这句话获得了更深的含义。在这里，序对应于质量项，竞争或相互兼容性可以从它们的对易性质推断出来。在这项资助计划中，我们将设计狄拉克系统中动态生成交织秩序的模型。我们制定的模型是通过建设免费的负号问题和大规模辅助场量子蒙特卡罗模拟可以提供近似免费的结果在多项式时间。它们将动态地产生量子自旋霍尔态，s波超导相，反铁磁绝缘体以及Kekulé价键固体。我们的目标是理解（2+1）维中任意两个相之间的跃迁，根据i）各个相的对称群和ii）相应质量项的代数性质。特别注意将放在紧急对称性，以及在低能量有效场论的拓扑和几何条件的发生。这些条款是在起源的相变超出金斯堡-朗道范式，其中一个阶段的拓扑缺陷进行的其他阶段的电荷和增殖的临界点。这项拨款建议的另一个方面是调查替代蒙特卡罗采样方案，旨在减少费米子系统的自相关时间耦合到虚时间缓慢变化的领域。

Intertwined orders can compete or be mutually compatible. This statement acquires a deeper meaning when perceived from the point of view of Dirac fermions. Here orders correspond to mass terms and competition or mutual compatibility can be inferred from their commutation properties. In this grant proposal, we will design models where intertwined orders are dynamically generated in Dirac systems. The models we formulate are by construction free of the negative sign problem and large scale auxiliary field quantum Monte Carlo simulations can provide approximation free results in polynomial time. They will dynamically generate quantum spin Hall states, s-wave superconducting phases, antiferromagnetic insulators as well as Kekulé valence bond solids. Our aim is to understand transitions between any two of these phases in (2+1)-dimensions in light of i) the symmetry group of the respective phases and ii) the algebraic properties of the corresponding mass terms. Special attention will be placed on emergent symmetries as well as on the occurrence of topological and geometrical terms in the low energy effective field theory. Such terms are at the origin of phase transitions beyond the Ginzburg-Landau paradigm where topological defects of one phase carry the charge of the other phase and proliferate at the critical point. Another aspect of this grant proposal is to investigate alternative Monte Carlo sampling schemes aiming at reducing autocorrelation times for systems of fermions coupled to slowly varying fields in imaginary time.