The one-dimensional XY model in a transverse field is a prototypical exactly solvable quantum system with nontrivial phase diagram, characterised by two different quantum phase transitions, i.e., ones at temperature zero. Using the Jordan-Wigner transformation, the model can always be mapped into a system of free fermions. In the thesis, we focus on the closed XY chain without external magnetic field and with odd number of spins, conducive to the phenomenon of frustration in case of the dominant antiferromagnetic interaction, i.e., the inability of minimising all of the local interactions simultaneously. This system was shown to exhibit interesting properties depending on the value of the anisotropy parameter ϕ determining the relative magnitude and sign of the x and y direction interactions. Also depending on this value, we make distinction between three phases, denoted ordered (1), mesoscopic (2) and incommensurate (3) based on the previously obtained results for each. After solving the XY model for its ground states and spectra via the Jordan- Wigner transformation and Bogoliubov rotation, we focus on calculating the one and two-point static and dynamic correlation functions after the system has undergone a global quench at t = 0, only changing its anisotropy parameter ϕ. In the t = 0 limit, we discuss the agreement of our results with known analytic limiting behaviour. Furthermore, using the dynamic expressions calculated through solving the time-evolution problem for the XY model, we explore the validity of the cluster decomposition hypothesis for all evolutions starting in one of the first two phases. In this way, several interesting results are obtained, namely the emergence of mesoscopic behaviour in the long-time regime for several evolutions and also a usual exponential decay of the cluster decomposition for the remaining ones. We discuss the rates of decay and emphasise that the evolutions starting in the third phase require additional subtlety to be analysed properly due to the breaking of translational invariance and are thus left for an upcoming paper.