一维量子体系的Anderson局域化现象和拓扑态的理论研究

This project aims at presenting a systematic study on the exotic quantum phenomena of topological states, Anderson localization and many-body localization in one-dimensional (1D) systems. A recent progress in condensed matter physics and cold atom physics allows one to build, control, and study the strongly interacting quantum degrees of freedom in the laboratory. These latest achievements have stimulated many studies in topological and Anderson localization phenomena in low-dimensional quantum models. The interplay between the topological phases and many-body localization and the interaction processes between the system and the environment will lead to many new physics which have not been investigated before...In this project, we will investigate the topological states, the Anderson localization and many-body localization phenomena in the 1D interacting system with p–wave superconducting pairing. With the help of quantum quench method, we will study the quantum dynamical properties of 1D topological models, which will show more insight on the dynamical quantum phase transition in the low-dimensional quantum systems. We will study the geometrical meaning of winding number and utilize it to characterize the topological phases in one-dimensional non-Hermitian systems. We will study the transport properties of non-Hermitian topological systems, which will help us to understand the interplay between quantum interference and parity-time symmetry in these systems. We plan to generalize and construct new topological models and find theoretical approaches beyond the mean-field description by including the effects of quantum fluctuations and quantum correlations. The new results obtained in the exotic ground states, topological excitations, localization, correlation effects, quantum dynamics, winding number and geometry phase, the dynamics quantum phase transition in 1D topological systems will have important implications in quantum many-body systems in condensed matter physics and cold atom physics.

本项目着重于一维相互作用拓扑体系的拓扑态性质、Anderson局域化和多体局域化现象，及其中的量子多粒子关联、动力学相变和非厄密量子效应的理论研究，揭示其中新的物理现象，为拓扑效应、多粒子关联理论和基于低维量子体系的量子调控和量子模拟提供坚实的理论基础。.最近在低维介观体系和超冷原子体系的重要的实验进展，为研究一系列新奇的量子多体模型提供了可以精确调控的平台。本项目将针对一维拓扑量子模型的新奇能带结构，考虑粒子间的相互作用、外加周期调制势、以及周围环境的影响，建立模型，有效地处理多粒子关联和局域化效应，并发展相关的数值计算方法，研究具有p波超导配对的一维相互作用系统的拓扑性质、Anderson局域化和多体局域化现象，量子动力学相变和拓扑相变现象，一维非厄密量子体系的拓扑态及其输运性质等前沿问题。

本课题的主要目标是研究一维相互作用拓扑体系的拓扑态性质、Anderson局域化和多体局域化现象，在本课题的资助下，在一维非厄密超晶格系统中的拓扑态，马赛克型(mosaic)的一维晶格系统的拓扑相、拓扑超导及Anderson局域化，准对易、非对易一维晶格系统的拓扑相和Anderson局域化等方向上从事理论研究工作。主要创新成果包括：..1）一维非厄密超晶格系统中的拓扑态的理论研究。构造了具有周期调制的非对称跃迁项的一维非厄密超晶格系统。发现当调制项的周期为偶数时，系统具有纯实的能谱，并且不会出现非厄密趋肤效应。而当调制项周期为奇数时，则能谱不能保证为实谱且系统中将出现非厄密趋肤效应。并且发现在具有准周期调制的系统中，稳定的拓扑边界态也可以存在，非厄密趋肤效应由于准周期调制的存在而被消除。进一步提出了利用拓扑电路来模拟这一模型的试验方案。我们提出的这个模型提供了一个研究非厄密拓扑系统的新平台。..2）构造了一类新型的非对角马赛克晶格模型，其中非对角调制是等间距的加在某些相邻格点之间的跃迁振幅上。发现具有零能模的拓扑相，并能构造出陈绝缘体。当这些非对角调制为非公度时，系统中会出现Anderson局域化现象。系统中的局域态完全由无公度的跃迁调制引起的，而不需要在位势能中的无序。这与常规的非对角模型存在较大的区别，我们的工作为研究低维系统中的拓扑态和安德森局域化提供了一种新的物理模型。..3）具有非对称跃迁的非厄米系统中的实能谱和非厄米趋肤效应的相变研究。解析证明并给出了系统能谱为实数或者虚数的条件和参数范围。发现对于不同的镶嵌型非对称跃迁周期，非厄米趋肤效应会出现相变。通过调节系统参数扫过临界点时，原本局域在一维晶格某一端的本征态会突然被移到另一端。这一变化伴随着系统能谱中的点状能隙的打开和闭合，因此非厄米趋肤效应的相变具有拓扑相变的特点。这一工作进一步揭示了非厄米系统的能谱和非厄米趋肤效应的新奇特性。