Statistical correlations of an anyon liquid at low temperatures

Topological phase transition and single/multi anyon dynamics of $Z_2$ spin liquid

Among the quantum many-body models that host anyon excitation and topological orders, quantum dimer models (QDM) provide a unique playground for studying the relation between single-anyon and multi-anyon continuum spectra. However, as the prototypical correlated system with local constraints, the generic solution of QDM at different lattice geometry and parameter regimes is still missing due to the lack of controlled methodologies. Here we obtain, via the newly developed sweeping cluster quantum Monte Carlo algorithm, the excitation spectra in different phases of the triangular lattice QDM. Ou…

电荷1/3任意子流体中的超导性和非费米液体金属

Superconductivity and non-Fermi liquid metals in a charge-1/3 anyon fluid

本文通过掺杂ν=2/3 Jain分数量子霍尔绝缘体得到电荷1/3任意子流体，发现复合费米子描述下的味对称配对态导致SC*态（电荷-2e凝聚与Z2拓扑序共存），而低掺杂近似SU(3)对称区域实现非费米液体Z3正交金属。

Statistical Interparticle Potential of an Ideal Gas of Non-Abelian Anyons

We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern-Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of Abelian anyons. In the Abelian case, the statistical potential depends on the statistical parameter and it has a "quasi-bosonic" behaviour for statistical parameter in the range (0,1/2) (non-monotonic with a minimum) and a "quasi-fermionic" behaviour for statistical parameter in the range (1/2,1) (monotonically decreasing without a minimum). In the non-Abelian case the behavior of the statistical …

非阿贝尔任意子增殖的统计力学与对称性：从形变到退相干

Statistical Mechanics and Symmetries of Non-Abelian Anyon Proliferation: From Deformation to Decoherence

通过统计力学模型和蒙特卡洛模拟，研究非阿贝尔任意子增殖导致拓扑序失稳的机制，发现两个非阿贝尔任意子物种的增殖会寄生凝聚共享的阿贝尔融合结果，破坏拓扑序。

任意子汤克斯-吉拉多气体的淬火动力学

Quench Dynamics of Anyon Tonks-Girardeau Gases

本文利用任意子-费米子映射方法研究强相互作用任意子在谐振子陷阱中的淬火动力学，发现密度分布与统计参数无关，陷阱关闭时动量分布呈对称费米子行为，频率淬火时出现不对称呼吸模式，并观察到约化单体密度矩阵的对称性破缺与重现。

哈密顿任意子的热力学及其在量子热机中的应用

Thermodynamics of Hamiltonian anyons with applications to quantum heat engines

提出一种通过对称性生成哈密顿量实现统计任意子的新方案，并展示其可动态调节统计特性、高效模拟，以及通过玻色化与费米化替代压缩膨胀冲程实现可逆功提取循环，从而提升热机性能。

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.

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.

Quantum walk of two anyons across a statistical boundary

We model a quantum walk of identical particles that can change their exchange statistics by hopping across a domain wall in a 1D lattice. Such a "statistical boundary" is transparent to single particles and affects the dynamics only by swapping multiple particles arriving together. We find that the two-particle interference is dramatically altered by reflections of these bunched waves at the interface, producing strong measurable asymmetries. Depending on the phases on the two sides, a bunched wavepacket can get completely reflected or split into a superposition of a reflected wave and an anti…

One-Dimensional Impenetrable Anyons in Thermal Equilibrium. I. Anyonic Generalization of Lenard's Formula

We have obtained an expansion of the reduced density matrices (or, equivalently, correlation functions of the fields) of impenetrable one-dimensional anyons in terms of the reduced density matrices of fermions using the mapping between anyon and fermion wavefunctions. This is the generalization to anyonic statistics of the result obtained by A. Lenard for bosons. In the case of impenetrable but otherwise free anyons with statistical parameter $κ$, the anyonic reduced density matrices in the grand canonical ensemble is expressed as Fredholm minors of the integral operator ($1-γ\hat θ_T$) with c…

Anyon Quantum Transport and Noise away from Equilibrium

We investigate the quantum transport of anyons in one space dimension. After establishing some universal features of non-equilibrium systems in contact with two heat reservoirs in a generalised Gibbs state, we focus on the abelian anyon solution of the Tomonaga-Luttinger model possessing axial-vector duality. In this context a non-equilibrium representation of the physical observables is constructed, which is the basic tool for a systematic study of the anyon particle and heat transport. We determine the associated Lorentz number and describe explicitly the deviation from the standard Wiedeman…