Year: 2025
Type: article
Abstract: Topological phase transitions beyond anyon condensation remain poorly understood. A notable example is the transition between the toric code (TC) and double semion (DS) phases, which has two distinct Z 2 topological orders in (2+1) dimensions [ ( 2 + 1 ) D ]. Previous studies reveal that the transition between them can be either first order or via an intermediate phase, thus the existence of a direct continuous transition between them remains a long-standing problem. Motivated by the fact that both phases can arise from condensing distinct anyons in the Z 4 topological order, we introduce a perturbed Z 4 quantum double (QD) model to study the TC-DS transition. We confirm the existence of a continuous ( 2 + 1 ) D XY* transition between the TC and DS phases by mapping it to a two-coupled quantum Ising model. Importantly, using the condensation order parameters and the area law coefficients of the Wilson loops, we further reveal that Z 4 anyons, fractionalized from the Z 2 topological orders, become deconfined at the transition between Z 2 topologically ordered phases. Our results open a path toward developing a theoretical framework for topological phase transitions beyond anyon condensation.
DOI: 10.1103/1bjs-mf2l
Authors: Qi Zhang, Wen-Tao Xu
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4417182893