Detecting the topological phases of the Kitaev model via complex network analysis

Patrick J. Wong, Andrew K. Mitchell

Xing-Yu Zhang, Qi Yang, Philippe Corboz +2 more

We investigate the quantum phases of higher-spin Kitaev models using tensor network methods. Our results reveal distinct bond-ordered phases for spin-1, spin-$\tfrac{3}{2}$, and spin-2 models. In all cases, we find translational symmetry breaking with unit cells being tripled by forming valence-bond orders. However, these three phases are distinct, forming plaquette order, topological dimer order, and non-topological dimer order, respectively. Our findings are based on a cross-validation between variational two-dimensional tensor network calculations: an unrestricted exploration of symmetry-broken states versus the detection of symmetry breaking from cat-state behavior in symmetry-restricted states. The origin of different orders can also be understood from a theoretical analysis. Our work sheds light upon the interplay between topological and symmetry-breaking orders as well as their detection via tensor networks.

Alfonso Maiellaro, Francesco Romeo, R. Citro

Razieh Mohseninia, Saeed S. Jahromi, Laleh Memarzadeh +1 more

The stability of the topological order phase induced by the ${\mathbb{Z}}_{3}$ Kitaev model, which is a candidate for fault-tolerant quantum computation, against the local order phase induced by the three-state Potts model is studied. We show that the low-energy sector of the Kitaev-Potts model is mapped to the Potts model in the presence of transverse magnetic field. Our study relies on two high-order series expansions based on continuous unitary transformations in the limits of small and large Potts couplings as well as mean-field approximation. Our analysis reveals that the topological phase of the ${\mathbb{Z}}_{3}$ Kitaev model breaks down to the Potts model through a first-order phase transition. We capture the phase transition by analysis of the ground-state energy, one-quasiparticle gap, and geometric measure of entanglement.

Isamu Ohnishi

Yucheng Wang

We investigate the evolutions of edge Majorana fermions (MFs), and we show that they can be used to characterize different topological phases and study topological phase transitions. For some limiting cases of the evolution process for the Kitaev chain model and the Su-Schrieffer-Heeger (SSH) model, we give analytical expressions of the survival probabilities (SPs) of the edge MFs. For a general case, we consider a dimerized Kitaev model as well as the Kitaev chain with disorder chemical potential, and we numerically calculate the SPs of two edge correlation MFs. Our results show that both of them are equal to zero, one of them is equal to zero at some times, or neither of them is equal to zero, which corresponds to the SSH-like topological, topological superconductor, and trivial phases, respectively.