Representation of Berry Phase by the Trajectories of Majorana Stars

Liu, H. D.; Fu, Libin

doi:10.1103/physrevlett.113.240403

Cited by 56 publications

(56 citation statements)

References 36 publications

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“…It is easy to verify the commutation relations for spin operators: [F i , F j ] = i ijk F k . Now the spin-1 state |ψ can be factorized as [58][59][60][61][62][63]…”

Section: Proof Of |C| ≤ 2 For Tdps Of Linear Hamiltoniansmentioning

confidence: 99%

Topological Triply Degenerate Points Induced by Spin-Tensor-Momentum Couplings

Hou

Zhang

et al. 2018

Phys. Rev. Lett.

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The recent discovery of triply degenerate points (TDPs) in topological materials has opened a new perspective toward the realization of novel quasiparticles without counterparts in quantum field theory. The emergence of such protected nodes is often attributed to spin-vector-momentum couplings. We show that the interplay between spin-tensor- and spin-vector-momentum couplings can induce three types of TDPs, classified by different monopole charges (C=±2, ±1, 0). A Zeeman field can lift them into Weyl points with distinct numbers and charges. Different TDPs of the same type are connected by intriguing Fermi arcs at surfaces, and transitions between different types are accompanied by level crossings along high-symmetry lines. We further propose an experimental scheme to realize such TDPs in cold-atom optical lattices. Our results provide a framework for studying spin-tensor-momentum coupling-induced TDPs and other exotic quasiparticles.

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“…It is easy to verify the commutation relations for spin operators: [F i , F j ] = i ijk F k . Now the spin-1 state |ψ can be factorized as [58][59][60][61][62][63]…”

Section: Proof Of |C| ≤ 2 For Tdps Of Linear Hamiltoniansmentioning

confidence: 99%

Topological Triply Degenerate Points Induced by Spin-Tensor-Momentum Couplings

Hou

Zhang

et al. 2018

Phys. Rev. Lett.

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“…The Majorana representation is used to determine geometric phase of spins (cf. [22,23]), in studying the symmetries of spinor Bose-Einstein condensates (cf. [24][25][26]), in geometrical representation of multi-qubit entangled states (cf.…”

Section: Introductionmentioning

confidence: 99%

Malevich’s Suprematist Composition Picture for Spin States

Man’ko

Markovich

2019

Entropy

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This paper proposes an alternative geometric representation of single qudit states based on probability simplexes to describe the quantum properties of noncomposite systems. In contrast to the known high dimension pictures, we present the planar picture of quantum states, using the elementary geometry. The approach is based on, so called, Malevich square representation of the single qubit state. It is shown that the quantum statistics of the single qudit with some spin j and observables are formally equivalent to statistics of the classical system with N 2 - 1 random vector variables and N 2 - 1 classical probability distributions, obeying special constrains, found in this study. We present a universal inequality, that describes the single qudits state quantumness. The inequality provides a possibility to experimentally check up entanglement of the system in terms of the classical probabilities. The simulation study for the single qutrit and ququad systems, using the Metropolis Monte-Carlo method, is obtained. The geometrical representation of the single qudit states, presented in the paper, is useful in providing a visualization of quantum states and illustrating their difference from the classical ones.

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“…The Majorana representation (MR), in which a pure state of a spin- system 1 , 2 can be precisely described as the trajectory of stars on a unit sphere, was proposed by Majorana in 1932 3 . Over the past decades, the MR has been proved to be a valuable method for many applications in quantum entanglement 4 – 10 , Bose-Einstein condensates 12 – 16 , 25 , and geometric phase 10 , 17 – 20 . In refs 10 , 20 , the Berry phase was studied by the stars and their loops on the Bloch sphere.…”

Section: Introductionmentioning

confidence: 99%

“…Over the past decades, the MR has been proved to be a valuable method for many applications in quantum entanglement 4 – 10 , Bose-Einstein condensates 12 – 16 , 25 , and geometric phase 10 , 17 – 20 . In refs 10 , 20 , the Berry phase was studied by the stars and their loops on the Bloch sphere. With the solid angles of the Majorana star loops, an intuitive relation between the Berry phase and Majorana stars’ trajectories on the Bloch sphere was given and it was shown that the Berry phase is determined by both the solid angles subtended by every Majorana star’s evolution path and the correlations between the stars 20 .…”

Section: Introductionmentioning

confidence: 99%

“…In refs 10 , 20 , the Berry phase was studied by the stars and their loops on the Bloch sphere. With the solid angles of the Majorana star loops, an intuitive relation between the Berry phase and Majorana stars’ trajectories on the Bloch sphere was given and it was shown that the Berry phase is determined by both the solid angles subtended by every Majorana star’s evolution path and the correlations between the stars 20 . Quantum entanglement were investigated by distributions and motions of these stars on the Bloch sphere 20 .…”

Section: Introductionmentioning

confidence: 99%

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The Exact Curve Equation for Majorana Stars

Feng

Liu

et al. 2017

Sci Rep

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Majorana stars are visual representation for a quantum pure state. For some states, the corresponding majorana stars are located on one curve on the Block sphere. However, it is lack of exact curve equations for them. To find the exact equations, we consider a superposition of two bosonic coherent states with an arbitrary relative phase. We analytically give the curve equation and find that the curve always goes through the North pole on the Block sphere. Furthermore, for the superpositions of SU(1,1) coherent states, we find the same curve equation.

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Representation of Berry Phase by the Trajectories of Majorana Stars

Cited by 56 publications

References 36 publications

Topological Triply Degenerate Points Induced by Spin-Tensor-Momentum Couplings

Topological Triply Degenerate Points Induced by Spin-Tensor-Momentum Couplings

Malevich’s Suprematist Composition Picture for Spin States

The Exact Curve Equation for Majorana Stars

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