Static and dynamic properties of quantum magnets
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Abstract
Quantum spin models provide the basis for understanding the complex phenomena associated with quantum magnetism. By tuning parameters describing the interactions between these spins, the onset of quantum fluctuations can drive a spin system into an exotic and complex “highly-correlated” state of matter, often displaying unusual, non-classical properties. These quantum phases typically involve the delicate interplay of an exponentially large number of degrees of freedom, posing substantial difficulties to studying using purely analytical tools. Numerical simulation of spin systems thus provides a key piece of this puzzle, allowing for the systematic study of quantum magnetism and the discovery of new quantum phenomena. To study quantum magnetism, physicists rely on lattice-models, regular grids hosting particles that interact with one another via quantum exchanges. These simplified models are used to study the low energy behavior of real quantum magnets and are typically more amenable to both analytic and numerical calculations, the latter of which being the main approach discussed in my thesis. Using quantum Monte Carlo simulations, I have studied various spin models with three main goals in mind: to explain observations made by experimental physicists, to predict how novel quantum systems may behave, and to provide benchmark calculations for the wide array of quantum devices and emulators that are entering the fray. In this thesis, I discuss the development and implementation of various numerical methods which I have used to contribute to all three of these branches of computational physics research. In particular, my thesis focuses on the calculation of static and dynamic properties of quantum magnetic materials, the different numerical tools used to do so, and the insights we gain by considering these two classes of observables in tandem. This thesis focuses of two models in particular: the Fully Frustrated Transverse Field Ising Model on the square-lattice and the two-dimensional Hubbard Model. I investigated both the ground-state properties and out-of-equilibrium dynamics of the former using a novel approach involving two order parameters, which capture different symmetries of the ordered phase. My work on the latter has focused on resolving the single-particle spectral function and the density of states by utilizing recent advancements in the stochastic analytic continuation method. I discuss my contributions to the development of the stochastic analytic continuation method and the application of this method to the Hubbard Model.
Description
2025
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Attribution 4.0 International