Quantum thermalisation and many-body localisation

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"How do quantum many-body systems thermalise? Can they ever fail to reach thermal equilibrium? Are the laws of thermodynamics and quantum mechanics compatible with each other? In spite of knowing the basic laws of quantum mechanics for more than 100 years, this basic question is yet to be thoroughly answered. In recent years there has been significant progress in understanding both thermalisation and its breakdown, a.k.a. many-body localisation (MBL). It is increasingly evident that the propagation of quantum information plays a crucial role in describing these phenomena. Furthermore, recent experimental progress in quantum control of solid state systems (NV centres, quantum dots) and synthetic quantum systems (cold atoms, trapped ions) has allowed exploration of these questions in the laboratory.This project will aim to study the properties of thermalisation and many-body localisation in spin chains and toy models by shedding new light on the entanglement structure of eigenstates and regimes of dynamics of multipartite entanglement. The candidate will use exact diagonalisation and many-bodyperturbation theory for calculating measures of entanglement such as negativity and mutual information. By using ideas of monogamy of entanglement from quantum information theory, a characteristic length scale for multipartite entanglement will be extracted to characterise the eigenstates and their dynamics in the two phase of matter. This will have potential implications for future dynamics experiments in quantum simulators."