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arXiv 1706.04793cond-mat.mes-hallquant-ph
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$ν=2/λ$上双层量子霍尔系统的Husimi函数和相空间分析

Husimi function and phase-space analysis of bilayer quantum Hall systems at $ν=2/λ$

M. Calixto, C. Peón-Nieto

摘要:

提出了分数填充因子为$ν=2/λ$的双层量子Hall(BLQH)系统基态相空间中的局域化测度,用以刻画任意$U(4)$ -同位旋$λ$的三个量子相(简称spin、canted和ppin).我们使用量子态的相干态(Bargmann)表示,作为8维格拉斯曼相空间$\mathbb{G}^4_{2}=U(4)/[U(2)\times U(2)]$(Halfman的2维球$\mathbb{S}^2=U(2)/[U(1)\times U(1)]$的高维推广)中的全纯函数。我们在整个相图中量化相空间中基态波函数的局部化(逆体积)(即,作为Zeeman、隧穿、层距等控制参数的函数)与Husimi函数二阶矩(一种表现为序参量的逆参与比)。然后,我们可视化不同的基态结构在相空间中的三个量子相位,倾斜的相位显示出更高的离域(薛定谔猫结构)比自旋和ppin相位,其中的基态是高度相干的。我们发现一个很好的协议之间的分析(变分)和数值对角化的结果。

英文摘要:

We propose localization measures in phase space of the ground state of bilayer quantum Hall (BLQH) systems at fractional filling factors $ν=2/λ$, to characterize the three quantum phases (shortly denoted by spin, canted and ppin) for arbitrary $U(4)$-isospin $λ$. We use a coherent state (Bargmann) representation of quantum states, as holomorphic functions in the 8-dimensional Grassmannian phase-space $\mathbb{G}^4_{2}=U(4)/[U(2)\times U(2)]$ (a higher-dimensional generalization of the Haldane's 2-dimensional sphere $\mathbb{S}^2=U(2)/[U(1)\times U(1)]$). We quantify the localization (inverse volume) of the ground state wave function in phase-space throughout the phase diagram (i.e., as a function of Zeeman, tunneling, layer distance, etc, control parameters) with the Husimi function second moment, a kind of inverse participation ratio that behaves as an order parameter. Then we visualize the different ground state structure in phase space of the three quantum phases, the canted phase displaying a much higher delocalization (a Schrödinger cat structure) than the spin and ppin phases, where the ground state is highly coherent. We find a good agreement between analytic (variational) and numeric diagonalization results.

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