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Motivated by the entanglement properties of low-energy states of local Hamiltonians I introduce matrix product states (MPS) as a variational ansatz for the study of one dimensional quantum many-body systems. Then I apply the MPS formalism to study 1+1 dimensional QED, also know as the massive Schwinger model. I explain how MPS are used to compute an approximation of the ground state and discuss its entanglement properties. Next, MPS are used to study non-equilibrium dynamics by a quench in the form of a uniform background electric field. When the electric background field is small, the results are explained by investigating the low-energy spectrum of the Hamiltonian. For larger values of the quench we observe thermalisation. Finally, I discuss how the MPS framework is generalised to higher dimensions and can be used to simulate real-time evolution.

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Boye Buyens, Ghent University
Seminarroom 0.02, ETP
Contact: Sebastian Diehl