From symmetry-protected topological order to Landau order

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.

8 pages, 1 table. Version v2 corresponds to the published version. It includes minor revisions and additional references

References in corpus (8)

• Detection of Symmetry Protected Topological Phases in 1D
• String order and symmetries in quantum spin lattices
• An order parameter for symmetry-protected phases in one dimension
• Topological order in 1D Cluster state protected by symmetry
• On topological phases of spin chains
• The hidden symmetry-breaking picture of symmetry-protected topological order
• String order and hidden topological symmetry in the SO(2n+1) symmetric matrix product states
• A discriminating string order parameter for topological phases of gapped SU(N) spin chains

Cited by in corpus (43)

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• Computational Power of Symmetry-Protected Topological Phases
• Non-Invertible Duality Transformation Between SPT and SSB Phases
• The hidden symmetry-breaking picture of symmetry-protected topological order
• Entanglement phases as holographic duals of anyon condensates
• Z_3 symmetry-protected topological phases in the SU(3) AKLT model
• General Lieb-Schultz-Mattis type theorems for quantum spin chains
• Gapped Phases with Non-Invertible Symmetries: (1+1)d
• Phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermions systems
• Wavefunctions of Symmetry Protected Topological Phases from Conformal Field Theories
• Study of anyon condensation and topological phase transitions from a ${\mathbb{Z}}_4$ topological phase using Projected Entangled Pair States
• Qudit quantum computation on matrix product states with global symmetry
• Chiral Haldane phases of SU(N) quantum spin chains in the adjoint representation
• On gapped phases with a continuous symmetry and boundary operators
• Generating Lattice Non-invertible Symmetries
• Symmetry-Protected Topological Entanglement
• Duality, Criticality, Anomaly, and Topology in Quantum Spin-1 Chains
• Symmetry protected topological phases beyond groups: The q-deformed Affleck-Kennedy-Lieb-Tasaki model
• Symmetry-protected topological order and negative-sign problem for SO(N) bilinear-biquadratic chains
• Hidden order and flux attachment in symmetry protected topological phases: a Laughlin-like approach
• Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems
• Novel families of $\mathrm{SU}(N)$ AKLT states with arbitrary self-conjugate edge states
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Quasi-exact quantum computation
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
• "Haldane" phases with ultracold fermionic atoms in double-well optical lattices
• Nonequilibrium symmetry-protected topological order: emergence of semilocal Gibbs ensembles
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• Symmetry protected topological phases in two-orbital SU(4) fermionic atoms
• Disentangling topological degeneracy in the entanglement spectrum of one-dimensional symmetry protected topological phases
• Self-$G$-ality in 1+1 dimensions
• Inferring Hidden Symmetries of Exotic Magnets from Detecting Explicit Order Parameters
• Duality and hidden symmetry breaking in the q-deformed Affleck-Kennedy-Lieb-Tasaki model
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking
• Topological and Error-Correcting Properties for Symmetry-Protected Topological Order
• Gauging Quantum Phases: A Matrix Product State Approach
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking
• Bosonic realization of SU(3) chiral Haldane phases