Numerical simulations of topological and exotic states of quantum matter

我们的研究目标是用数值方法来揭示费米子系统中的相关驱动效应。拓扑学是我们理解相和相变的核心。例如，已知在1+1维度中，半整数和整数自旋链的物理性质因作用中存在或不存在拓扑项而不同。这个概念可以推广到2+1维。我们研究的目标之一是研究一个2+1维的模型，在这个模型中，在量子相变附近出现的拓扑项可以作为模型参数的函数被打开和关闭。我们将继续研究电子-声子相互作用，特别是集中在Su-Schrieffer-Heeger模型的对称推广上。在这里，我们将使用一种新的方法，我们可以把声子积分出来。我们的目标是理解这个模型的物理性质，从辅助跳变状态，它映射到Z2晶格规范理论，到跳变调制比跳变本身小的状态。这两个主要课题将由另外两个方向的研究加以补充。我们将在双曲晶格上进行相关电子系统模型的计算。我们的目的是研究在弯曲空间中是否会出现新的相关诱导效应。声子在热输运中起着关键作用。我们的目标是利用我们在模拟Su-Schrieffer-Heeger哈密顿量方面的进展来研究相内和跨相变的热输运。我们在有限晶格上的所有精确数值计算都将使用我们的辅助场量子蒙特卡罗算法的开源实现来进行。

The goal of our research is to use numerical methods to unravel correlation driven effects in fermionic systems. Topology is at the center of our understanding of phases and phase transitions. For example it is known that in 1+1 dimensions, the physics of half-integer and integer spin chains differ by the presence or absence of a topological term in the action. This notion can be generalized to 2+1 dimensions. One of the aims of our research is to investigate a model in 2+1 dimensions where topological terms, that emerge in the vicinity of quantum phase transitions, can be switched on and off as a function of a model parameter. We will pursue our work on the electron-phonon interactions and in particular concentrate on a symmetry allowed generalization of the Su-Schrieffer-Heeger model. Here we will use a novel approach in which we can integrate out the phonons. We aim to understand the physics of this model from the assisted-hopping regime, where it maps onto Z2 lattice gauge theories, to the regime where the modulation of the hopping is small as compared to the hopping itself. These two main subjects will be supplemented by research along two other directions. We will carry out calculations of models of correlated electron systems on hyperbolic lattices. Our aim here is to investigate if novel correlation induced effects emerge in curved spaces. Phonons in thermal transport play a pivotal role. We aim to use our advances in simulations of the Su-Schrieffer-Heeger hamiltonian to investigate thermal transport in phases and across phase transitions. All our numerically exact calculations on finite lattices will be carried out with our open source implementation of the auxiliary field quantum Monte Carlo algorithm.