Classifying quantum phases using matrix product states and projected entangled pair states

We give a classification of gapped quantum phases of one-dimensional systems in the framework of matrix product states (MPS) and their associated parent Hamiltonians, for systems with unique as well as degenerate ground states and in both the absence and the presence of symmetries. We find that without symmetries, all systems are in the same phase, up to accidental ground-state degeneracies. If symmetries are imposed, phases without symmetry breaking (i.e., with unique ground states) are classified by the cohomology classes of the symmetry group, that is, the equivalence classes of its projective representations, a result first derived by Chen, Gu, and Wen [Phys. Rev. B 83, 035107 (2011)]. For phases with…

• NS
  National Science Foundation

  Awards: 0803371, PHY-0803371
• GA
  Gordon and Betty Moore Foundation

  Award: PHY-0803371
• CI
  California Institute of Technology
• DF
  Deutsche Forschungsgemeinschaft
• AR
  Army Research Office

  Awards: W911NF-09-1-0442, W911NF