Topological phase transition of deformed ℤ3 toric code
- 1Korea University
Abstract
We investigate topological phase transitions in a family of deformed ℤ3 toric-code wavefunctions prepared from a cluster state by local deformations and projective measurements. Their norms map to the Q=3 Potts model for single-parameter deformations and to a three-state Ashkin–Teller-like (AT3) construction with two independent four-spin couplings in the general case. Projected entangled-pair-state (PEPS) and variational uniform matrix-product-state (VUMPS) calculations identify the toric-code (TC) phase and phases in which electric (e) anyons are confined or condensed. These phases are separated by critical structures with central charges c=4/5, 8/5, and isolated c=1 antiferromagnetic (AFM) endpoints. A normalized finite-distance e-anyon pair-state norm provides a Fredenhagen–Marcu-type check of the confinement boundary, while the topological data of the quantum double D(ℤ3) imply a topological entanglement entropy γ=log3 throughout the gapped toric-code phase. Relative to the ℤ2 case, the absence of sign-change folding leaves the AFM endpoints unfolded, and the extreme deformation reaches square ice with an emergent U(1) one-form symmetry, Hilbert-space fragmentation, and exact scar configurations.
Related
- Shot-based variational simulation of the toric code phase transition: Energy, global entanglement, and noise resilience
- Long-Range Toric Code: Finite-Temperature Topological Order in Two Dimensions
- Topological Quantum Error-Correcting Thresholds of a Symmetry-Enriched Toric Code
- Gibbs-state phases beyond microscopic symmetry breaking: A phase invariant for the 3D toric code
- New topological phase transitions in κ-deformed ϕ4 lattice models
BibTeX
@article{oh2026topological,
title = {{Topological phase transition of deformed $\mathbb Z_3$ toric code}},
author = {Yun-Tak Oh and Hyun-Yong Lee},
journal = {SciPost Physics},
year = {2026},
month = nov,
doi = {10.21468/scipostphys.21.5.109},
url = {https://doi.org/10.21468/scipostphys.21.5.109},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Topological phase transition of deformed ℤ_3 toric code
AU - Yun-Tak Oh
AU - Hyun-Yong Lee
PY - 2026
DA - 2026/11/02
JO - SciPost Physics
DO - 10.21468/scipostphys.21.5.109
UR - https://doi.org/10.21468/scipostphys.21.5.109
AB - We investigate topological phase transitions in a family of deformed ℤ_3 toric-code wavefunctions prepared from a cluster state by local deformations and projective measurements. Their norms map to the Q=3 Potts model for single-parameter deformations and to a three-state Ashkin–Teller-like (AT_3) construction with two independent four-spin couplings in the general case. Projected entangled-pair-state (PEPS) and variational uniform matrix-product-state (VUMPS) calculations identify the toric-code (TC) phase and phases in which electric (e) anyons are confined or condensed. These phases are separated by critical structures with central charges c=4/5, 8/5, and isolated c=1 antiferromagnetic (AFM) endpoints. A normalized finite-distance e-anyon pair-state norm provides a Fredenhagen–Marcu-type check of the confinement boundary, while the topological data of the quantum double D(ℤ_3) imply a topological entanglement entropy γ=log3 throughout the gapped toric-code phase. Relative to the ℤ_2 case, the absence of sign-change folding leaves the AFM endpoints unfolded, and the extreme deformation reaches square ice with an emergent U(1) one-form symmetry, Hilbert-space fragmentation, and exact scar configurations.
SN - 2542-4653
ER -