Ground-state phase diagram for a system of interacting, $D(D_3)$ non-Abelian anyons

$\mathbf{Z}_{n}$ clock models and chains of $so(n)_2$ non-Abelian anyons: symmetries, integrable points and low energy properties

We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking similarities are observed between certain $\mathbf{Z}_n$ quantum clock models, spin chains generalizing the Ising model, and chains of non-Abelian anyons constructed from the $so(n)_2$ fusion category for odd $n$, both subject to periodic boundary conditions. In spite of the differences between these two types of quantum chains, e.g.\ their Hilbert spaces being spanned by tensor products of local spin states or fusion…

Floquet Majorana Edge Mode and Non-Abelian Anyons in a Driven Kitaev Model

We theoretically study laser driven nonequilibrium states in the Kitaev honeycomb model with a magnetoelectric cross coupling. We show that a topological spin liquid with a gapless chiral edge mode emerges when we apply an elliptically or circularly polarized laser. This is a strongly correlated quantum spin version of the Floquet topological insulator. In the topological phase, the edge mode is made from Majorana fermions and the bulk has gapped non-Abelian anyon excitations.

Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons

Thermodynamic properties of chiral spin liquids are investigated for a variant of the Kitaev model defined on a decorated honeycomb lattice. Using the quantum Monte Carlo simulation, we find that the model exhibits a finite-temperature phase transition associated with the time reversal symmetry breaking, in both topologically trivial and nontrivial regions. While changing the exchange constants, the phase transition changes from continuous to discontinuous one, apparently correlated with the change in the excitations from Abelian to non-Abelian anyons. We show this coincidence by computing the…

Bethe Ansatz for 1D interacting anyons

This article gives a pedagogic derivation of the Bethe Ansatz solution for 1D interacting anyons. This includes a demonstration of the subtle role of the anyonic phases in the Bethe Ansatz arising from the anyonic commutation relations. The thermodynamic Bethe Ansatz equations defining the temperature dependent properties of the model are also derived, from which some groundstate properties are obtained.

Generalized exclusion statistics and degenerate signature of strongly interacting anyons

We show that below the degenerate temperature the distribution profiles of strongly interacting anyons in one dimension coincide with the most probable distributions of ideal particles obeying generalized exclusion statistics (GES). In the strongly interacting regime the thermodynamics and the local two-particle correlation function derived from the GES are seen to agree for low temperatures with the results derived for the anyon model using the thermodynamic Bethe Ansatz. The anyonic and dynamical interactions implement a continuous range of GES, providing a signature of strongly interacting …

阿贝尔和非阿贝尔拓扑码的整数线性规划译码器

Integer Linear Programming Decoder for Abelian and Non-Abelian Topological Codes

该研究针对任意拓扑序，提出基于整数线性规划的译码器，其在三类拓扑序的纠错任务中性能优于多数现有译码器，可应用于容错量子计算。

Collective states of interacting Fibonacci anyons

We show that chains of interacting Fibonacci anyons can support a wide variety of collective ground states ranging from extended critical, gapless phases to gapped phases with ground-state degeneracy and quasiparticle excitations. In particular, we generalize the Majumdar-Ghosh Hamiltonian to anyonic degrees of freedom by extending recently studied pairwise anyonic interactions to three-anyon exchanges. The energetic competition between two- and three-anyon interactions leads to a rich phase diagram that harbors multiple critical and gapped phases. For the critical phases and their higher symm…

非阿贝尔任意子的测量诱导临界性：受监控的黄金链

Measurement-induced criticality for non-Abelian anyons: The monitored golden chain

该研究将受监控的非阿贝尔任意子链动力学映射到随机张量网络，发现其具有非幺正CFT特征，确立受监控黄金链为托里克码量子临界点的非阿贝尔推广，为非阿贝尔学习问题提供了基础示例。

The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics

The low energy properties of the one-dimensional anyon gas with $δ$-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter $α$ is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of $α$ in the dispersion relations.

Anyon-Net上涌现的手征边缘态

Chiral Edge States Emerging on Anyon-Net

本文提出基于对称性的Anyon-Net晶格模型构建方法，利用任意子链与MTC在微观层面保证精确对称性，并通过张量网络模拟验证Ising和Fibonacci非阿贝尔任意子拓扑相中的手征边缘态。