Duality and hidden symmetry breaking in the q-deformed Affleck-Kennedy-Lieb-Tasaki model
arXiv:2403.09287 · doi:10.21468/SciPostPhysCore.7.4.078
Abstract
We revisit the question of string order and hidden symmetry breaking in the q-deformed AKLT model, an example of a spin chain that possesses generalized symmetry. We first argue that the non-local Kennedy-Tasaki duality transformation that was previously proposed to relate the string order to a local order parameter leads to a non-local Hamiltonian and thus does not provide a physically adequate description of the symmetry breaking. We then present a modified non-local transformation which is based on a recently developed generalization of Witten's Conjugation to frustration-free lattice models and capable of resolving this issue.
26 pages, 2 figures
References in corpus (17)
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
- Non-Invertible Higher-Categorical Symmetries
- Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
- Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
- Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
- Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
- Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
- Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
- Non-Invertible Duality Transformation Between SPT and SSB Phases
- Dualities in one-dimensional quantum lattice models: topological sectors
- Duality, Criticality, Anomaly, and Topology in Quantum Spin-1 Chains
- Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
- Symmetry protected topological phases beyond groups: The q-deformed Affleck-Kennedy-Lieb-Tasaki model
- The matrix product representation for the q-VBS state of one-dimensional higher integer spin model
- Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain
- Entanglement Properties of a Higher-Integer-Spin AKLT Model with Quantum Group Symmetry