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1イオン異方性を伴うS=1 XXZ鎖の四重臨界点

Shuichi Shiraishi

Published Mar 25, 2025• 0 citations
OpenAlex

Abstract

In quantum many body systems, phase transitions can occur even at absolute zero temperature due to quantum fluctuations.In particular, in low dimensional systems, the effects of fluctuations are strong, and despite the apparent simplicity of the model, it has a variety of non-trivial critical phenomena.We research the ground state of the S = 1 XXZ spin chain with single-ion anisotropy.The Hamiltonian of this model is expressed as

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In quantum many body systems, phase transitions can occur even at absolute zero temperature due to quantum fluctuations.In particular, in low dimensional systems, the effects of fluctuations are strong, and despite the apparent simplicity of the model, it has a variety of non-trivial critical phenomena.We research the ground state of the S = 1 XXZ spin chain with single-ion anisotropy.The Hamiltonian of this model is expressed as
This thesis addresses the surprising features of zero-temperature statics and dynamics of several spin glass models, including correlations between soft spins that arise spontaneously during avalanches, and the discovery of localized states that involve the presence of two-level systems. It also presents the only detailed historiographical research on the spin glass theory. Despite the extreme simplicity of their definition, spin glasses display a wide variety of non-trivial behaviors that are not yet fully understood. In this thesis the author sheds light on some of these, focusing on both the search for phase transitions under perturbations of Hamiltonians and the zero-temperature properties and responses to external stimuli. After introducing spin glasses and useful concepts on phase transitions and numerics, the results of two massive Monte Carlo campaigns on three-dimensional systems are presented: The first of these examines the de Almeida Thouless transition, and proposes a new finite-size scaling ansatz, which accelerates the convergence to the thermodynamic limit. The second reconstructs the phase diagram of the Heisenberg spin glass with random exchange anisotropy
It is known that arrays of trapped ions can be used to efficiently simulate a variety of many-body quantum systems. Here we show how it is possible to build a model representing a spin chain interacting with bosons that is exactly solvable. The exact spectrum of the model at zero temperature and the ground-state properties are studied. We show that a quantum phase transition occurs when the coupling between spins and bosons reaches a critical value, which corresponds to a level crossing in the energy spectrum. Once the critical point is reached, the number of bosonic excitations in the ground state, which can be assumed as an order parameter, starts to be different from zero. The population of the bosonic mode is accompanied by a macroscopic magnetization of the spins. This double effect could represent a useful resource for phase transition detection since a measure of the phonon can give information about the phase of the spin system. A finite-temperature phase diagram is also given in the adiabatic regime.