论文标题
最低兰道级的比例不变性
Scale Invariance in the Lowest Landau Level
论文作者
论文摘要
我们表明，Haldane引入的离散的对振幅$ a_m $是TAN两体触点的角度分析的概括，它参数介绍了原子量子气中通用的短距离相关性。两对幅度提供了最低的Landau级别（LLL）的翻译不变和旋转不变状态的完整描述，这些状态都可压缩和不可压缩。为了领先非交互高温限制以外的非平凡秩序，它们可以根据haldane pseudoptential参数进行分析确定$ v_m $，该$ V_M $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $。此外，我们表明，对于接触互动$ \ simg_2δ{（2）}（{\ bf x}）$，在经典级别上是不变的，指导中心坐标的非偏置性会导致commutator $ i [hat hat { =（2 + \ ell \ partial_ \ ell）\ hat {h} _ {\ rm lll} $，带有扩张算子$ \ hat {d} _r $在lll中，在缺乏磁场的情况下代替了跟踪异常。相互作用引起的规模不变性破裂导致呼吸陷阱中呼吸模式的有限频移，该谐波陷阱描述了不同的Landau级别之间的过渡，其强度是根据相关的无限耦合常数$ \ tilde {G tilde {g} _2 $估算的。
We show that the discrete set of pair amplitudes $A_m$ introduced by Haldane are an angular-momentum resolved generalization of the Tan two-body contact, which parametrizes universal short-range correlations in atomic quantum gases. The pair amplitudes provide a complete description of translation-invariant and rotation-invariant states in the lowest Landau level (LLL), both compressible and incompressible. To leading nontrivial order beyond the non-interacting high-temperature limit, they are determined analytically in terms of the Haldane pseudopotential parameters $V_m$, which provides a qualitative description of the crossover towards incompressible ground states for different filling factors. Moreover, we show that for contact interactions $\sim g_2 δ^{(2)}({\bf x})$, which are scale invariant at the classical level, the non-commutativity of the guiding center coordinates gives rise to a quantum anomaly in the commutator $i [\hat{H}_{\rm LLL}, \hat{D}_R] = (2 + \ell \partial_\ell) \hat{H}_{\rm LLL}$ with the dilatation operator $\hat{D}_R$ in the LLL, which replaces the trace anomaly in the absence of a magnetic field. The interaction-induced breaking of scale invariance gives rise to a finite frequency shift of the breathing mode in a harmonic trap, which describes transitions between different Landau levels, the strength of which is estimated in terms of the relevant dimensionless coupling constant $\tilde{g}_2$.
