利用自旋退相干探测多体系统在参数复平面上的相变性质

Phase transition is one of the most important issues in many-body physics. In 1952, T. D. Lee and C. N. Yang investigated the analytic properties of partition function of a many-body system in the complex plane of the magnetic field and discovered that the complex magnetic fields which make partition function vanishes, termed Lee-Yang zeros, determine the phase transition point and all the critical exponents. Since Lee-Yang zeros occur only at the complex plane of magnetic fields, they were not regarded as observable. In 2012, the applicant and collaborators found that central spin decoherence which is coupled to a classical spin system can be used to probe Lee-Yang zeros and in the thermodynamic limit spin decoherence could present time-domain phase transitions where the critical times correspond to the Yang-Lee edge singularities of the free energy in the complex plane of magnetic field. Based on this finding, this project will study (1) Finite-size scaling analysis and universality classes of the time-domain phase transitions in the decoherence of the probe spin which is coupled to a classical spin model. (2) Scenario for probing the partition function zeros and edge singularities in quantum many-body systems. (3) Schemes for observing partition function zeros and time-domain phase transitions in real materials. Studies in this project may be helpful for understanding the mechanism of time-domain phase transitions and building up foundations for metrology.

相变是多体物理研究中最重要的问题之一。1952年李政道和杨振宁研究了多体系统的配分函数在磁场复平面上的解析性质并发现使配分函数为零的复数磁场（称为李-杨零点）决定了系统的相变点和临界指数等。由于李-杨零点只发生在磁场的复平面上，长久以来被认为不可测量。 2012年申请人和合作者利用一个探测自旋与经典自旋系统耦合，发现探测自旋退相干信号可以观测自旋系统配分函数的李-杨零点并且在热力学极限下自旋退相干会发生时间相变，其临界时间对应于系统自由能在磁场复平面上的杨-李边界奇点。本项目在这个发现的基础上拟研究（1）与经典自旋多体系统耦合时探测自旋退相干发生时间相变的有限尺寸标度行为和普适类别；（2）量子多体系统配分函数零点以及边界奇点观测方案；（3）设计实际物理体系来观测配分函数零点和时间相变。本项目的研究有助于理解时间相变发生的物理机制并为设计精密测量的新方案提供理论基础。

我们按照项目的研究计划，项目进展比较顺利，取得了一定的研究成果，已经发表了14篇SCI文章。在项目执行期间，我们研究了（1）与经典自旋多体系统耦合时探测自旋退相干发生时间相变的有限尺寸标度行为和普适类别；（2）量子多体系统配分函数零点以及边界奇点观测方案；（3）设计实际物理体系来观测配分函数零点和时间相变。本项目的研究有助于理解时间相变发生的物理机制并为设计精密测量的新方案提供理论基础。