Final PhD Oral Examination (Thesis Title: “Fluctuations and Phase Transitions in Quantum Ising Systems”)

Event Date and Time: 
Mon, 2016-08-15 09:00 - 11:00
Room 200, Graduate Student Centre
Local Contact: 
Physics and Astronomy, UBC
Intended Audience: 

The quantum Ising model is perhaps the simplest possible model of a quantum magnetic material. Despite its simplicity, its versatility and wide range of applications, from quantum computation, to combinatorial optimization, to biophysics, make it one of the most important models of modern physics. In this thesis, we develop a general framework for studying quantum Ising systems with an arbitrary single ion hamiltonian, with emphasis on the effects of quantum fluctuations, and the quantum phase transition between paramagnetic and ferromagnetic states that occurs when a magnetic field is applied transverse to the easy axis of the system.

The magnetic insulating crystal LiHoF4 is a physical realization of the quantum Ising model, with the additional features that the dominant coupling between spins is the long range dipolar interaction, and each electronic spin is strongly coupled to a nuclear degree of freedom. In this thesis, we present an effective model for LiHoF4 that fully incorporates the long range dipolar interaction and the nuclear degrees of freedom, and we analyze the effects of the nuclear spins on the quantum phase transition. We find the lowest energy crystal field excitation in the system is gapped at the quantum critical point by the presence of the nuclear spins, with spectral weight being transferred down to a lower energy electronuclear mode that fully softens to zero at the quantum phase transition. Furthermore, we present a toy model, the spin half spin half model, that illustrates the effects of an anisotropic hyperfine interaction on a quantum Ising system. We find the critical transverse field is increased when the longitudinal hyperfine coupling is dominant, as well as an enhancement of both the longitudinal electronic susceptibility and an applied longitudinal field.

In addition, we present a general field theoretic formalism for incorporating the effects of fluctuations beyond the random phase approximation in quantum Ising systems. We find that additional nuclear degrees of freedom, or any other regualr on site interaction, do not fundamentally alter the critical properties of a quantum Ising system. This formalism is used to calculate corrections to the magnetization of LiHoF4.

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