强关联电子体系及拓扑物态研究

In the past several years, topological states of quantum matter has attracted increasing attentions and interest in condensed matter physicists since the discoveries of topological insulators. Based on the theoretical works that we have done in the past several years, we will contitune to work on quantum states of matter with topology and strong correlations. Our main research interest is focused on the following directions.We shall employ renormalization group theory, spin-fluctuation exchange theory, and dynamic mean field theory to investigate mechanism of unconventional superconductivity and other related theoretical issues in 2D and 3D electronic systems. We shall focus on microscopic mechanism favoring topological superconductivity and look for Majorana zero modes which can be experimentally detected and manipanated. We shall continue our studies in theories of quantum spin liquids. We shall perform determinant quantum Monte Carlo simulations to investigate the half-filled Hubbard model on certain lattices, which escape the minus sign problem of quantum Monte Carlo, to find quantum spin liquid ground states and design real materials to potentially realize these exotic quantum states of matter in Nature. We shall explore intrinsic connections between quantum spin liquids and the mechanism of high temperature superconductivity. We will study topological classification of non-Abelian quantum states of matter in the presense of symmetries and interactions. We shall study the interplay between topology and lattice symmetry in classification and characterizations of those states of matter.We shall also study quantum entanglement in gapless quantum systems and explore the intrinsic and universal relations between entanglement entropy and topoloy as well as geometry.

在过去的几年，随着拓扑绝缘体的发现，拓扑量子物态激发了许多凝聚态物理学家的兴趣及研究热情。结合我们近年来的工作基础，我们将继续开展拓扑量子物态以及强关联体系的研究，主要研究如下方向。我们继续采用重整化群理论、自旋激发交换理论、及动态平均场等方法来研究二维及三维体系中相互作用引起的非常规超导机制及其它基本理论问题，并着重于探索形成拓扑超导的微观机制，并探讨在实验上实现能被探测及有效调控的马约那纳费米子。我们将继续研究量子自旋液体的理论，探索其和高温超导机制的内在联系，并用量子蒙特卡罗方法研究2D晶格的半满Hubbard模型，探寻量子自旋液体的存在及其材料实现。我们将探索具有对称性的相互作用体系中非-Abelian拓扑物态分类及其物性表征等基本问题，并将拓扑性质和晶体晶格对称性相结合。同时我们将研究无能隙体系中的量子纠缠，并阐明纠缠熵和拓扑及几何的关系。

本项目主要研究强关联电子体系和拓扑物态中的新奇量子和拓扑现象，项目负责人在提出新型量子蒙特卡洛方法、研究高温超导机理的有效模型、提出新颖量子相变和局域化相变、拓扑超导和马约拉纳费米子等方面取得了创新性的成果。主要学术贡献如下：一、原创性地提出马约拉纳表象的量子蒙特卡洛方法并应用这一新型的量子蒙特卡洛方法解决了系列重要的强关联物理问题，包括发现了拓扑超导体边界态量子临界点的演生超对称性、费米子诱导的新型量子临界点、和单狄拉克锥体系超导量子相变点的演生超对称性，应用量子蒙特卡洛模拟阐明了电声子相互作用可以显著提高超导转变温度；二、理论上发现三维外尔半金属的超导量子相变点具有演生时空超对称性，是三维凝聚态体系中实现演生超对称性的首个范例，并进一步提出了凝聚态体系中实现超对称量子电动力学的新途径；三、率先提出一类严格可解模型来研究新型多体局域化相变及应用实空间重整化群方法首次研究了准周期体系中的多体局域化相变。在本项目的支持下，共完成高水平学术论文35篇，其中包括10篇Phys. Rev. Lett.、2篇Nature Communications、1篇Science Advances。本项目支持完成的论文总被引600余次。