From symmetry-protected topological order to Landau order

Understand

Focusing on the particular case of the discrete symmetry group Z_N x Z_N, we establish a mapping between symmetry protected topological phases and symmetry broken phases for one-dimensional spin systems.

• It is realized in terms of a non-local unitary transformation which preserves the locality of the Hamiltonian.
• We derive the image of the mapping for various phases involved, including those with a mixture of symmetry breaking and topological protection.
• Our analysis also applies to topological phases in spin systems with arbitrary continuous symmetries of unitary, orthogonal and symplectic type.