Detection of gapped phases of a 1D spin chain with onsite and spatial symmetries

Abstract

We investigate the phase diagram of a quantum spin-1 chain whose Hamiltonian is invariant under a global onsite $A_4$, translation and lattice inversion symmetries. We detect different gapped phases characterized by SPT order and symmetry breaking using matrix product state order parameters. We observe a rich variety of phases of matter characterized by a combination of symmetry breaking and symmetry fractionalization and also the interplay between the onsite and spatial symmetries. Examples of continuous phase transitions directly between topologically nontrivial SPT phases are also observed.

19 pages, 6 figures

References in corpus (10)

• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• The iTEBD algorithm beyond unitary evolution
• A classification of symmetry enriched topological phases with exactly solvable models
• String order and symmetries in quantum spin lattices
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
• String flux mechanism for fractionalization in topologically ordered phases
• Symmetry-protected topological phases and transition in a frustrated spin-$\frac{1}{2}$ XXZ chain
• Identifying quantum phases from injectivity of symmetric matrix product states

Cited by in corpus (5)

• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Symmetry-protected topological phases with uniform computational power in one dimension
• Dynamical engineering of interactions in qudit ensembles
• Entanglement and the density matrix renormalisation group in the generalised Landau paradigm
• Pivoting through the chiral-clock family