Topological phase transition of anyon systems

Wen-Tao Xu, José Garre-Rubio, Norbert Schuch

Topological phases - systems with a global ordering in the entanglement - exhibit exotic excitations known as anyons which can display highly nontrivial (non-Abelian) statistics. Through transitions between such phases, these anyons can undergo rather surprising changes. Perhaps most surprisingly, one anyon can split into two or more anyons, some of which might condense or become confined. The authors propose here a complete set of order parameters which allow one to extract the full information about how the properties of anyons change through phase transitions, and to apply them to a range of topological phase transitions.

Cao, Zhenbin, Liu Liu +3 more

Carlo A. Trugenberger

Zheng-Wei Zuo, Guo-Ling Li, Liben Li

We theoretically investigate topological properties of the one-dimensional superlattice anyon-Hubbard model, which can be mapped to a superlattice bose-Hubbard model with an occupation-dependent phase factor by fractional Jordan-Wigner transformation. The topological anyon-Mott insulator is identified by topological invariant and edge modes using exact diagonalization and the density matrix renormalization group algorithm. When only the statistical angle is varied and all other parameters are fixed, a statistically induced topological phase transition can be realized, which provides insights into the topological phase transitions. What's more, we give an explanation of the statistically induced topological phase transition. The topological anyon-Mott phases can also appear in a variety of superlattice anyon-Hubbard models.

Qi Zhang, Wen-Tao Xu

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.

M. A. Contínentino