密级
博士学位论文
作者姓名：许霄琰
中国科学院物理研究所
学位类别：理学博士现代货币数量论
学科专业：理论物理
研究所：中国科学院物理研究所
2017年5月
Quantum Monte Carlo simulations
of fermion-boson lattice systems
By
教育财会研究Xiao Yan Xu
A Dissertation Submitted to
The University of Chinese Academy of Sciences In partial fulfillment of the requirement
For the degree of
Doctor of Science
石门五中穿孔机Institute of Physics
Chinese Academy of Sciences
May,2017
摘要
摘要
横膈膜费米子-玻子耦合格点模型是一类描写玻量子涨落与费米子耦合的格点模型，它可以直接刻画强关联体系中序参量的量子涨落，对于研究量子相变与量子临界区内临界行为，热力学性质，可能出现哪些新的相等等具有重要意义。在本论文中，我们主要讨论费米子耦合格点模型的量子蒙特卡洛研究，包括狄拉克费米子与伊辛向列序涨落的耦合诱导的拓扑量子相变，巡游铁磁量子临界点上的非费米液体行为以及在改进量子蒙特卡洛方法方面的尝试。 首先我们通过大尺度量子蒙特卡洛模拟研究了狄拉克半金属中相互作用驱动的拓扑相变。狄拉克费米子之间的相互作用通过与伊辛场的耦合产生，具有铁磁相互作用的伊辛场的量子涨落由横场调控.我们具体研究了不同横场和不同耦合强度下的相图。在弱的或者中等强度耦合情况下，我们观测到了二阶的伊辛相变，以及具有不同拓扑的狄拉克半金属间的一级拓扑相变.有趣的是，在拓扑相变发生处，费米面上有节线产生，同时观测到具有SO(4)对称性的玻涨落.在强耦合区域，这两个相边界会合并成一个一级相变的相边界.
其次，我们还研究了巡游体系铁磁量子临界点上的非费米液体行为.我们构造了一个费米子与伊辛铁磁临界涨落耦合的二维格点模型，并利用无符号问题的量子蒙特卡洛计算进行研究．该模型实现了连续量子相变．与其它类似的巡游体系量子临界点相比，我们的铁磁量子临界点附近在很低的温度下都没有超导出现，使得该系统成为研究巡游体系量子临界行为的理想平台.重要的是，我们在该铁磁量子临界点附近观测到了清晰的非费米液体行为.与此同时，该临界点的行为与Hertz-Millis-Moriya预测的有些类似，但是，更为仔细的标度分析表明，该临界点可能属于一个新的普适类，与(2+1)维伊辛相变和Hertz-Millis-Moriya都不同.
最后，我们提出了一个新的量子蒙特卡洛方法，即自学习量子蒙特卡洛方法，用于解决量子蒙特卡洛计算中的(临界)慢化问题.我们在行列式量子蒙特卡洛的框架下讨论了具体实现，并计算了玻场与费米面耦合的问题.由于该方法超高的加速，我们在临界点上可以计算100×100的格子，并能够获得精确的临界指数.
i
费米子-玻子耦合格点体系的量子蒙特卡洛模拟
关键词：行列式量子蒙特卡洛，拓扑相变，临界行为，非费米液体，自学习量子蒙特卡洛
ii
Abstract
Abstract
Fermion-boson lattice model is a model which describe the coupling between fermion and bosonic quantumfluctuations.As the model directly captures the quantumfluctuations of order parameter in correlated electron systems,it is meaningful for exploring the quantum critical behavior,thermodynamics and many possible new phases in quantum critical region.In this thesis,we will mainly discuss quantum Monte Carlo simulation of fermion-boson lattice model, including topological phase transition driven by the coupling between the Dirac fermion and Ising nematic quantumfluctuations,non-fermi-liquid at itinerant ferromagnetic quantum critical point as well as our attempt on the improvements on the algorithm of quantum Monte Carlo.
Atfirst,interaction-driven topological phase transitions in Dirac semimetals are investigated by means of large-scale quantum Monte Carlo simulations.The interaction among Dirac fermions is introduced by coupling them to Ising spins that realize the quantum dynamics of the two-dimensional transversefield Ising model.The ground state phase diagram,in which the tuning parameters are the transversefield and the coupling between fermion and Ising spins,is determined. At weak and interm
ediate coupling,a second-order Ising quantum phase tran-sition and afirst-order topological phase transition between two topologically distinct Dirac semimetals are observed.Interestingly,at the latter,the Dirac points smear out to form nodal lines in the Brillouin zone,and collective bosonic fluctuations with SO(4)symmetry are strongly enhanced.At strong coupling, these two phase boundaries merge into afirst-order transition.
Secondly,we studied the non-fermi-liquid behavior at the itinerant ferro-magnetic quantum critical point.We construct a two-dimensional lattice model of fermions coupled to Ising ferromagnetic criticalfluctuations.Using extensive sign-problem-free quantum Monte Carlo simulations,we show that the model realizes a continuous itinerant quantum phase transition.In comparison with other similar itinerant quantum critical points,our quantum critical point shows
TSL2550
iii
豫公网安备41160202000603
站长QQ:729038198
关于我们
投诉建议