强关联电子体系及拓扑物态研究

项目名称： 强关联电子体系及拓扑物态研究

项目编号： No.11474175

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 姚宏

作者单位： 清华大学

项目金额： 90万元

中文摘要： 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。

中文关键词： 凝聚态理论；强关联体系；拓扑绝缘体；高温超导

英文摘要： 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.

英文关键词： condensed matter theory;strongly correlated systems;topological insulators;high temperature supeconductivity