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@PHDTHESIS{Iqbal:723457,
      author       = {Iqbal, Mohsin},
      othercontributors = {Schuch, Norbert and Weßel, Stefan},
      title        = {{T}opological phenomena in tensor network states of quantum
                      spin systems},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      reportid     = {RWTH-2018-224210},
      pages        = {1 Online-Ressource (v, 138 Seiten)},
      year         = {2018},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2018},
      abstract     = {The focus of our investigations in this thesis is quantum
                      spin systems in two dimensions. We examine phase transitions
                      between topologically distinct phases of quantum matter
                      using the framework of tensor network states. We study the
                      phenomena of anyon condensation and confinement in the
                      context of tensor network states where these two notions
                      offer a robust probe to characterize the universal features
                      of quantum phase transitions. We do a comprehensive study of
                      the numerical methods enabled by the tensor network
                      formalism for the study of quantum phase transitions. We map
                      out the phase diagram of certain exotic phases of quantum
                      matter (namely the $D(\mathbb{Z}_4)$ quantum double, the
                      toric code, and the double semion model) and identify the
                      order and the universality classes of the phase transitions
                      between these distinct topological phases. We analyze the
                      phase boundaries of the toric code and the double semion
                      model which exhibit first and second order phase
                      transitions. We investigate the class of
                      $\mathbb{Z}_2$-invariant tensor network states while taking
                      in to account the spin rotation and lattice symmetries. The
                      resulting tensor network states allow us to map the phase
                      diagram of $\mathbb{Z}_2$ spin liquids. The behavior of the
                      system at the phase boundaries of $\mathbb{Z}_2$ spin liquid
                      is governed by the condensation of spinons and visions. We
                      also present our preliminary findings regarding the
                      $\mathbb{Z}_4$-invariant tensors with $SU(2)$ symmetry. This
                      approach enables us to study the spin liquid states of the
                      toric code and the double semion model in a unified
                      framework. We give a local tensor description for the
                      approximate ground states of the Heisenberg antiferromagnet
                      on the kagome lattice by using the variational manifolds of
                      just three and five parameters in the gapped $\mathbb{Z}_2$
                      spin liquid phase. The approximation of the ground states we
                      construct have an energy density that is remarkably close to
                      the results from the state-of-the-art density matrix
                      renormalization group and the exact diagonalization method.
                      By analyzing the deconfinement of anyonic excitations, we
                      also present our findings regarding the vicinity of the
                      variational ground state in gapped $\mathbb{Z}_2$ spin
                      liquid phase.},
      cin          = {135820 / 130000},
      ddc          = {530},
      cid          = {$I:(DE-82)135820_20140620$ / $I:(DE-82)130000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2018-224210},
      url          = {https://publications.rwth-aachen.de/record/723457},
}