格点玻色系统中奇异量子态的量子蒙特卡洛模拟

Lattice boson system is one of the most important objectives in the study of many-body physics. With the rapid development of experimental techniques, particularly due to the realization of superfluid to Mott-insulator transition by Greiner et al. in cold bosons in an optical lattice, lattice boson systems are attracting more and more attention. The superfluid and Mott-insulator states are already well understood. Other unusual quantum states, such as supersolid, pair supersolid and Haldane insulator, are also considered to deserve intensive research. However, the microscopic mechanism and formation condition of these quantum states are not yet clear. In this project, we shall detect the existence of supersolid, pair supersolid and Haldane-insulator states in typical lattice boson systems, by using quantum Monte Carlo methods which work with continuous imaginary time as well as traditional treatments including exact diagonalization and mean-field calculation. Furthermore, we shall determine the properties of relevant phase transitions and critical behaviors. On this basis, we shall investigate world-line configurations and various excitation spectra to explore the microscopic mechanism of the unusual quantum states, and figure out the formation condition of these quantum states. In addition to answering fundamental physical questions, we shall precisely measure the two-body correlation function in momentum space which serves as an important reference for the experimental study of cold bosons in optical lattice.

格点玻色系统是多体物理研究的重要对象之一。随着实验技术的迅速发展，特别是Greiner等人实现光晶格中玻色冷原子系统的超流-Mott绝缘态转变后，格点玻色系统正受到越来越多的关注。目前，人们对超流态和Mott绝缘态已有较为深刻的理解。然而，以超固态、配对超固态和Haldane绝缘态为代表的其它奇异量子态的研究价值虽被广泛认同，但其微观机制和形成条件尚不明确。在本项目中，我们将运用连续虚时框架内的量子蒙特卡洛方法，并辅以精确对角化和平均场计算等传统技术手段，在几个典型的格点玻色系统中探测超固态、配对超固态和Haldane绝缘态的存在，并判定相关的相变与临界行为。在此基础上，结合对世界线位形和多种激发谱的分析，我们将探讨这些奇异量子态的微观机制和形成条件。在着眼于回答基本物理问题的同时，我们还将精确测定动量空间内的两体关联函数，为光晶格上的玻色冷原子实验研究提供重要参考。

格点玻色系统新奇量子态的研究具有高度的理论价值。此外，随着实验技术的迅速发展，特别是Greiner等人实现光晶格中玻色冷原子系统的超流-Mott绝缘态转变后，格点玻色系统已成为量子模拟的重要对象。目前，人们对超流态和Mott绝缘态已有较为深刻的理解。然而，以超固态、配对超固态和Haldane绝缘态为代表的其它奇异量子态的研究价值虽被广泛认同，但其微观机制和形成条件尚不明确。在本项目中，我们运用连续虚时框架内的量子蒙特卡洛方法，并辅以精确对角化和平均场计算等传统技术手段，在几个典型的格点玻色系统中探测到超固态、配对超固态、Haldane绝缘态和团簇Mott绝缘态的存在，同时给出若干典型玻色系统的基态相图，并判定相关的相变与临界行为。与此同时，我们还在格点玻色系统中探索到“无序导致有序”和弱一级相变等新奇物理现象，刻画了晶格几何特性对相变与临界现象的一般作用。在此基础上，结合对世界线位形和多种激发谱的分析，我们探讨了这些奇异量子态的微观机制和形成条件。在着眼于回答基本物理问题的同时，我们还精确测定了动量空间内的两体关联函数，从而为光晶格上的玻色冷原子实验研究提供重要参考。

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