Topological quantum phase transition in an extended Kitaev spin model

Topological footprints of the 1D Kitaev chain with long range superconducting pairings at a finite temperature

We study the 1D Kitaev chain with long range superconductive pairing terms at a finite temperature where the system is prepared in a mixed state in equilibrium with a heat reservoir maintained at a constant temperature $T$. In order to probe the footprint of the ground state topological behavior of the model at finite temperature, we look at two global quantities extracted out of two geometrical constructions: the Uhlmann and the interferometric phase. Interestingly, when the long-range effect dominates, the Uhlmann phase approach fails to reproduce the topological aspects of the model in the …

有序通量构型下Kitaev自旋纳米带的拓扑表征

Topological Characterization of Kitaev Spin Nanoribbons with Ordered Flux Configurations

本研究对Kitaev自旋纳米带进行拓扑表征，绘制不同通量构型下的Majorana自旋子相图，发现锯齿形与扶手椅形纳米带在相变次数及对通量构型敏感性上存在差异，并以绕数作为拓扑不变量。

From Ising model to Kitaev Chain -- An introduction to topological phase transitions

In this general article, we map the one-dimensional transverse field quantum Ising model of ferromagnetism to Kitaev's one-dimensional p-wave superconductor, which has its application in fault-tolerant topological quantum computing. Mapping Pauli's spin operators of transverse Ising chain to spinless fermionic creation and annihilation operators by Inverse Jordan-Wigner transformation leads to a Hamiltonian form closely related to Kitaev Chain, which exhibits topological phase transition where phases are characterized by different topological invariant that changes discontinuously at the trans…

Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions

We explore the behaviour of the disconnected entanglement entropy (DEE) across the topological phases of a long range interacting Kitaev chain where the long range interactions decay as a power law with an exponent $α$. We show that while the DEE may not remain invariant deep within the topologically non-trivial phase when $α<1$, it nevertheless shows a quantized discontinuous jump at the quantum critical point and can act as a strong marker for the detection of topological phase transition. We also study the time evolution of the DEE after a sudden quench of the chemical potential within the …

Kitaev磁体中拓扑激发的磁热效应

Magnetocaloric Effect of Topological Excitations in Kitaev Magnets

本文提出利用量子自旋液体的分数化拓扑激发实现亚开尔文制冷，并用张量网络计算揭示Kitaev模型中铁磁$Z_2$涡旋制冷及反铁磁无能隙相的高自旋熵。

Spread Complexity and Topological Transitions in the Kitaev Chain

A number of recent works have argued that quantum complexity, a well-known concept in computer science that has re-emerged recently in the context of the physics of black holes, may be used as an efficient probe of novel phenomena such as quantum chaos and even quantum phase transitions. In this article, we provide further support for the latter, using a 1-dimensional p-wave superconductor - the Kitaev chain - as a prototype of a system displaying a topological phase transition. The Hamiltonian of the Kitaev chain manifests two gapped phases of matter with fermion parity symmetry; a trivial st…

Network topology: detecting topological phase transitions in the Kitaev chain and the rotor plane

We propose a novel network measure of topological invariants, called small-worldness, for identifying topological phase transitions of quantum and classical spin models. Small-worldness is usually defined in the study of social networks based on the best known discovery that one can find a short chain of acquaintances connecting almost any two people on the planet. Here we demonstrate that the small-world effect provides a useful description to distinguish topologically trivial and non-trivial phases in the Kitaev chain and accurately capture the Kosterlitz-Thouless transition in the rotor pla…

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.

Extended Kitaev chain with longer-range hopping and pairing

We consider the Kitaev chain model with finite and infinite range in the hopping and pairing parameters, looking in particular at the appearance of Majorana zero energy modes and massive edge modes. We study the system both in the presence and in the absence of time reversal symmetry, by means of topological invariants and exact diagonalization, disclosing very rich phase diagrams. In particular, for extended hopping and pairing terms, we can get as many Majorana modes at each end of the chain as the neighbors involved in the couplings. Finally we generalize the transfer matrix approach useful…

Exact results for spin dynamics and fractionization in the Kitaev Model

We present certain exact analytical results for dynamical spin correlation functions in the Kitaev Model. It is the first result of its kind in non-trivial quantum spin models. The result is also novel: in spite of presence of gapless propagating Majorana fermion excitations, dynamical two spin correlation functions are identically zero beyond nearest neighbor separation, showing existence of a gapless but short range spin liquid. An unusual, \emph{all energy scale fractionization}of a spin -flip quanta, into two infinitely massive $π$-fluxes and a dynamical Majorana fermion, is shown to occur…

非厄米基塔耶夫链中的纠缠相变

Entanglement phase transitions in non-Hermitian Kitaev chains

本研究揭示非厄米基塔耶夫链中由损耗诱导的纠缠相变，发现稳态纠缠熵的标度行为可区分拓扑相，并建立谱、拓扑与纠缠性质间的联系。

Topological quantum phase transitions and criticality in a longer-range Kitaev chain

In an attempt to theoretically investigate the quantum phase transition and criticality in topological models, we study Kitaev chain with longer-range couplings (finite number of neighbors) as well as truly long-range couplings (infinite number of neighbors). We carry out an extensive topological characterization of the momentum space to explore the possibility of obtaining higher order winding numbers and analyze the nature of their stability in the model. The occurrences of phase transitions from even-to-even and odd-to-odd winding numbers are observed with decreasing longer-rangeness in the…