Topological phase transition of deformed toric code
arXiv:2603.09107
The paper studies how deformations of the Z₃ toric-code wavefunction lead to topological phase transitions, mapping the problem to Potts and Ashkin‑Teller models and using tensor‑network methods to identify confined, condensed, and topologically ordered phases.
Abstract
We investigate topological phase transitions in a family of deformed toric-code wavefunctions prepared from a cluster state by local deformations and projective measurements. Their norms map to the Potts model for single-parameter deformations and to a three-state Ashkin--Teller-like (AT) 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 () anyons are confined or condensed. These phases are separated by critical structures with central charges , , and isolated antiferromagnetic (AFM) endpoints. A normalized finite-distance -anyon pair-state norm provides a Fredenhagen--Marcu-type check of the confinement boundary, while the topological data of the quantum double imply a topological entanglement entropy throughout the gapped toric-code phase. Relative to the case, the absence of sign-change folding leaves the AFM endpoints unfolded, and the extreme deformation reaches square ice with an emergent one-form symmetry, Hilbert-space fragmentation, and exact scar configurations.
v2: revised in response to referee reports at SciPost Physics; additions and replacements highlighted in blue