UROP Proceedings 2020-21

School of Science Department of Physics 71 Application of Machine Learning in Physics Supervisor: LIU Junwei / PHYS Student: CHEN You-chiuan / PHYS-IRE Course: UROP4100, Fall Utilization of auxiliary fields is a standard technique in applications of quantumMonte Carlo algorithms when decomposition of many-body interactions between indistinguishable particles is feasible. In this report, we first review how auxiliary fields are introduced with the Hubbard model as example. Next, we discuss how auxiliary fields come with the notorious sign problem, and some conditions under which the absence of the sign problem is guaranteed. At last, we raise a new perspective: even when there is no sign problem, a quantum Monte Carlo algorithm using Metropolis sampling may be less efficient than that using random sampling because of the singularities in Green’s functions induced by auxiliary fields. Theoretical Study of Properties of Real Materials Supervisor: LIU Junwei / PHYS Student: KWOK Yuk Lam / PHYS-IRE Course: UROP1100, Summer We aim at studying about the band structure of graphene ribbon using Python. First, the Hamiltonian from tight-binding model is used, the Bloch Hamiltonian of a 2D graphene is constructed, and its band structure is calculated. Then we do the same thing on graphene ribbon, which band structure depends on its edge shape. We also investigate the effect of ribbon width on the bandgap and edge states. After that, we take the spinorbit coupling into consideration by adding a second term into the Hamiltonian. The strength of spinorbit coupling is varied, and its effect on the band structures is discussed. Axion-like Dark Matter Supervisor: LIU Tao / PHYS Student: LOU Xuzixiang / PHYS-IRE Course: UROP1100, Spring This report reviews my UROP 1100 project, Detecting Axion-like Dark Matter with Pulsar Polarization Array, in Spring Semester, 2021. As a popular dark matter candidate, axions or axion-like particles are currently under extensive research. Axion-like dark matter in our galaxy behaves like a classical scalar field, and light traveling through it receives a rotation in the linear polarization angle. Based on this effect, we propose to detect axionlike dark matter using linearly-polarized pulsar light, taking into account both temporal and spacial correlations of the polarization angles. We use PPTA pulsar polarization data to set 95% C.L. limits on the axion-photon coupling.

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