周期驱动量子伊辛模型中非热统计的形成与抑制  

Formation and suppression of nonthermal statistics in peridically driven quantum Ising models

作　　者：江璐冰 李宁轩 吉凯 Jiang Lu-Bing;Li Ning-Xuan;Ji Kai(Department of Physics,Shanghai Normal University,Shanghai 200234,China)

机构地区：[1]上海师范大学物理系,上海200234

出　　处：《物理学报》2020年第14期42-49,共8页Acta Physica Sinica

基　　金：上海市浦江人才计划(批准号:17PJ1407400)资助的课题.

摘　　要：在一维伊辛模型基础上,采用严格对角化方法研究孤立量子系统在周期驱动下量子微正则统计形成与抑制的条件.研究表明用纵向磁场驱动时伊辛模型不能形成量子微正则统计,用横向磁场驱动时可出现部分形成的趋势,如果同时在伊辛模型内引入局域随机磁场则可完全实现.量子微正则统计分布在系统中的形成或抑制取决于弗洛凯算符对量子系统作用的效果,可通过信息熵定量描述,信息熵越大则时间演化越能有效地遍历希尔伯特空间,从而形成量子微正则统计.这一行为是孤立量子系统可被热化的反映.In classic statistical physics,an isolated system corresponds to a constant energy shell in the phase space,which can be described by the microcanonical ensemble.While,for an isolated quantum system,the conventional treatment is to subject the system to a narrow energy window in the Hilbert space instead of the energy shell in classical phase space,and then confine the participating eigen states of system wave function in the narrow window,so that the microcanonical ensemble can be recovered in the framework of quantum mechanics.Apart from the traditional theory,there is a more self-consistent description for the isolated quantum system,that is,the quantum microcanonical(QMC)ensemble.The QMC ensemble abandons the narrow energy window assumption,and allows all the eigen states to contribute to the system wave function on condition that the system average energy is fixed at a given value.At the same time,the total occupation probability of these eigen states is conserved to unity.The most probable probability distribution obtained in the Hilbert space for an isolated quantum system according to the constraints specified above is called the QMC statistics.There is a clear difference between the QMC distribution and the traditional Gibbs distribution having an exponential form.Through the external periodic drives,an isolated quantum system may produce the QMC distribution,which is a consequence of the interplay between internal origins and external drives.In this paper,we investigate the conditions for the formation and suppression of QMC distribution by using the exact diagonalization method based on the one-dimensional Ising model.We start with the one-dimensional Ising model and focus on three different cases of periodic drives:systems under vertical(along the z axis),horizontal(along the x axis),horizontal magnetic field together with random internal(along the y axis)magnetic field.For all these three cases,the external magnetic fields are set to be ordinary rectangular pulses and the Gibbs distributions are take

关 键 词：微正则系综 伊辛模型 弗洛凯表象 热化 

分 类 号：O414.211[理学—理论物理]