Numerical studies of quantum lattice systemsTools Michailidis, Alexios (2017) Numerical studies of quantum lattice systems. PhD thesis, University of Nottingham.
AbstractThe research work in this thesis is based on strongly interacting quantum lattice systems. The biggest part of research was conducted using stateoftheart tensor network simulations. Tensor networks provide efficient and highly accurate representations of quantum states when any simply connected patch of the quantum state is slightly entangled. Matrix Product States (MPS) is a tensor network representation for quantum states which is quasiexact for onedimensional systems when entanglement entropy of any bipartition of the state follows ``arealaw". Projected Entangled Pair States (PEPS) is the extension of MPS for higher dimensional systems, where entanglement entropy arealaw is nontrivial. These formalisms and their relevant ground state optimization techniques, Density Matrix Renormalization Group (DMRG) for MPS and Simple Update (SU) with Tensor Renormalization Group (TRG) for PEPS are thoroughly analysed.
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