| Summary: | 碩士 === 國立政治大學 === 應用物理研究所 === 102 === The study of quantum phase transitions in magnetic materials has been a major focus of modern condensed-matter physics. In this thesis we study the zero-temperature phase diagram and critical properties of the antiferromagnetic Ising spin chain in transverse and longitudinal magnetic fields by quantum Monte Carlo simulations. The nearest-neighbor Ising interaction favors staggered magnetic ordering along the z axis. As we vary a transverse magnetic field h^x, which is a quantum mechanical parameter, the Ising spin chain will undergo a quantum phase transition from an antiferromagnetic ordered ground state when the interaction dominates to a paramagnetic ground state when the applied transverse field dominates. A magnetic field h^z applied along the Ising axis can further destabilize antiferromagnetic order. We consider two types of couplings: (i) the homogeneous case where the interaction and the magnetic fields are site-independent; (ii) the disordered case where site-to-site variations of the interaction and the transverse field are random. For the homogeneous case, the antiferromagnetic phase and the paramagnetic phase are separated by a critical line in (h^x, h^z) plane, ending at the multicritical point with h^x=0 where a classical first-order transition occurs. It is found numerically that the critical line for h^x>0 belongs to the universality class of the two-dimensional classical Ising model. For the disordered case, the quantum critical point for h^z=0 is of unconventional infinite-randomness type with infinite dynamic exponent. In a finite longitudinal field, our numerical results suggest that the sharp global quantum phase transition is destroyed by smearing.
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