两次淬火下横场中XY链的动力学量子相变  

Dynamical quantum phase transitions in transverse field XY chain after a double quench

作　　者：符浩 曹凯源 钟鸣[1] 童培庆[1,2] Fu Hao;Cao Kai-Yuan;Zhong Ming;Tong Pei-Qing(School of Physics and Technology,Nanjing Normal University,Nanjing 210023,China;Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems,Nanjing Normal University,Nanjing 210023,China)

机构地区：[1]南京师范大学物理科学与技术学院,南京210023 [2]南京师范大学,江苏省大规模复杂系统数值模拟重点实验室,南京210023

出　　处：《物理学报》2021年第18期36-46,共11页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11975126,11575087)资助的课题.

摘　　要：研究了两次淬火下横场中XY链的动力学量子相变.两次淬火是指系统的Hamilton量先由H_(0)淬火到H_(1),演化一段时间T后再由H_(1)淬火到H_(2).由于横场中XY链存在两种不同的量子相变(Ising相变和各向异性相变),因此主要讨论淬火路径对横场中XY链的动力学量子相变的影响,发现第2次淬火后系统发生动力学量子相变的临界时间存在三种典型的情形.情形Ⅰ对应于临界时间在一定的T范围内出现,它与由H_(0)淬火到H_(1)的临界时间相联系.情形Ⅱ对应于临界时间在任意T时总是出现,它与由H_(0)直接淬火到H_(2)的临界时间相联系.情形Ⅲ对应于临界时间也在任意T时总是出现,它同时与由H_(0)淬火到H_(1)以及由H_(0)直接淬火到H_(2)的临界时间相联系.还发现两次淬火都经过同一类相变点时,第2次淬火后只会出现情形I对应的临界时间.而两次淬火经过不同类相变点时,第2次淬火后的临界时间会出现上述三种情形中的任意两种,它与淬火路径有关.Nonequilibrium dynamics of quantum many-body systems have achieved rapid progress from boththeoretical and experimental perspectives. Recently, dynamical quantum phase transitions (DQPTs), whichdescribe the nonanalytic behaviors of physical quantities during the time evolution, have attracted a lot ofinterest. The most studied protocol to drive the system out of equilibrium is via a quantum quench. Recently,the DQPTs in the Ising chain and ANNNI chain after double quench are studied. Double quench means that the Hamiltonian of the system is abruptly changed from H_(0) to H_(1),and then abruptly changed from H_(1) to H_(2) after a evolutionary time T. One can control at will whether or not DQPTs appear after the second quench by varying T. In this paper, we study the DQPTs arising from a double quench in the anisotropic XY chain in a transverse field. The anisotropic XY chain in a transverse field has two kinds of quantum phase transitions (Ising transition and anisotropic transition). We discuss mainly the effects of quench paths on the DQPTs of the transverse field XY chain. By calculating the rate function of the Loschmidt echo and Fisher zeros, we find that there are three typical types of the critical times of DQPTs in the plane of the T and the evolution time t. Type Ⅰ of critical times, which occurs only in a certain range of T, is related to the protocol of the Hamiltonian abruptly changed from H_(0) to H_(1). Type Ⅱ of critical times, which occurs all the time, is related to the protocol of the Hamiltonian abruptly changed from H_(0) to H_(2). Type Ⅲ of critical times, which occurs all the time, is related to the protocols of the Hamiltonian abruptly changed from H_(0) to H_(1) and H_(0) to H_(2). When the double quench paths pass through the same kind of transition point, only the critical times corresponding to Type Ⅰ will appear after the second quench. When the double quench paths pass through different kinds of transition points, the critical times after the second quench will appear any two

关 键 词：动力学量子相变 横场中 XY 链 量子淬火 

分 类 号：O413[理学—理论物理]