一维量子多体系统的热力学与局域化研究

基于若干一维精确可解模型的可积性，研究在一维相互作用体系中远离平衡态的热力学输运性质以及无序或周期驱动导致的多体局域化现象。首先分析少体相互作用体系的精确本征能谱的统计性质，从多体角度考虑一维量子体系中广义流体力学描述的热输运问题，在周期驱动的系统中模拟黎曼零点并研究多体局域化问题，进一步利用机器学习基于精确解构造量子多体波函数对不同的量子相及其动力学演化进行鉴别。本项目将建立从少体到多体可积系统的物理图景，在热力学和统计物理方面为两者建立联系，属于原始创新性的课题，可能的突破包括多体系统关联函数的计算以及黎曼零点问题的物理实现。

We investigate the out-of-equilibrium thermodynamics and many-body localization in the interacting one-dimensional quantum few- and many-body systems based on their integrability. Starting from the energy level spacing statistics of the few-body system, we extend the research into the generalized hydrodynamics in order to understand the ballistic transport properties when the two semi-infinite halves are joined together, and furthermore into the many body localization of Floquet engineered systems, with a possibility of simulating the zeros of Riemann's zeta function in periodically driven system. We then resort to the machine learning scheme for many-body quantum state wavefunction for the identification of the quantum phases and their dynamical evolution, taking the integrable Gaudin-Yang model as a numerical benchmark. This project will build a physical picture from few body systems to many-body integrable systems, and establish a connection between them in thermodynamics and statistical physics. It is an original and innovative subject with possible breakthroughs including the calculation of the correlation function of the many-body system and the physical verification of the Riemann hypothesis.