Noncommutative geometry, extended W∞ algebra, and Grassmannian solitons in multicomponent quantum Hall systems
Noncommutative geometry, extended W∞ algebra, and Grassmannian solitons in multicomponent quantum Hall systems
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DOI：
10.1103/physrevb.67.125314
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发表时间：
2002-09
影响因子：
3.7
通讯作者：
Z. F. Ezawa;G. Tsitsishvili;K. Hasebe
中科院分区：
文献类型：
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作者：
Z. F. Ezawa;G. Tsitsishvili;K. Hasebe
非交换几何支配着量子霍尔（QH）效应的物理学。我们引入第二量子化密度算符的Weyl序来探索电子在最低朗道能级的动力学。我们以整数填充因子$\ensuremath{\nu}=kl~N.$分析了由N分量电子组成的QH系统，基本代数是SU(N)扩展${W}_{\ensuremath{\infty}}.$，其具体特征是非交换几何通过产生交换库仑相互作用导致SU(N)量子相干性的自发发展。有效哈密顿量为Grassmannian ${G}_{N,k}$ sigma模型，动力场为Grassmannian ${G}_{N,k}$场，描述了$k(N\ensuremath{-}k)$复杂Goldstone模和一种拓扑孤子（Grassmannian孤子）。
Noncommutative geometry governs the physics of quantum Hall (QH) effects. We introduce the Weyl ordering of the second quantized density operator to explore the dynamics of electrons in the lowest Landau level. We analyze QH systems made of N-component electrons at the integer filling factor $\ensuremath{\nu}=kl~N.$ The basic algebra is the SU(N)-extended ${W}_{\ensuremath{\infty}}.$ A specific feature is that noncommutative geometry leads to a spontaneous development of SU(N) quantum coherence by generating the exchange Coulomb interaction. The effective Hamiltonian is the Grassmannian ${G}_{N,k}$ sigma model, and the dynamical field is the Grassmannian ${G}_{N,k}$ field, describing $k(N\ensuremath{-}k)$ complex Goldstone modes and one kind of topological solitons (Grassmannian solitons).