In this master’s thesis, we explore quantum integrability and chaos through the study of the 2D Heisenberg model, which is an important extension of the well-known 1D Heisenberg model. Quantum integrability is defined using Algebraic Bethe ansatz, and we demonstrate that the 2D Heisenberg model is integrable when considering only horizontal interactions. We give an alternative definition of quantum integrability using Poisson statistics, where a system is considered integrable if the statistics of its spectrum follow the Poisson distribution. Quantum chaos is defined using random matrix theory, where a system is said to be chaotic if the spectral statistics follow one of the Wigner-Dyson distributions. These definitions are valid only when all spatial symmetries in the system have been removed. We describe the symmetries of the 2D Heisenberg model and explain how to remove them. Finally, we focus on numerical analysis and demonstrate, through the use of level spacing ration and the spectral form factor, that integrability breaks down in the system as the strength of the vertical interactions increases, indicating a transition to chaotic dynamics.
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