Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
From symmetry-protected topological order to Landau order
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abstract
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. This is achieved by identifying suitable subgroups Z_N x Z_N in all these groups, together with a bijection between the individual classes of projective representations.
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The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.
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Symmetry Spans and Enforced Gaplessness
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
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Self-$G$-ality in 1+1 dimensions
The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.