Intertwined orders and exotic phase transitions in Dirac fermions

相互交织的订单可以相互竞争，也可以相互兼容。从狄拉克·费米子的观点来看，这一说法具有更深的含义。在这里，有序对应于质量项，竞争或相互兼容可以从它们的交换性质中推断出来。在这份赠款提案中，我们将设计在狄拉克系统中动态生成相互交织的订单的模型。我们构造的模型没有负号问题，大规模辅助场量子蒙特卡罗模拟可以在多项式时间内提供无近似结果。它们将动态地产生量子自旋霍尔态、S波超导相、反铁磁绝缘体以及凯库尔价键固体。我们的目的是根据i)各个相的对称群和ii)相应质量项的代数性质来理解(2+1)维中任意两个相之间的跃迁。在低能有效场论中，我们将特别关注突现对称性以及拓扑和几何项的出现。这些项是超出金兹堡-朗道范式的相变的起源，其中一个相的拓扑缺陷携带另一个相的电荷，并在临界点扩散。这项拨款提案的另一个方面是研究可选的蒙特卡罗抽样方案，旨在减少费米子系统在虚时间内耦合到缓慢变化的场的自相关时间。

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.