一维么正关联费米子的Heisenberg对称性和集体模
Heisenberg Symmetry and Collective Modes of One Dimensional Unitary Correlated Fermions
摘要：
相关的费米子多粒子系统，接近无限的散射长度，揭示了一个潜在的海森堡对称性在一维，相比之下，$SO(2,1)$对称性在二维。这有助于从相互作用到非相互作用系统的精确映射，无论有没有谐波陷阱，并解释了波函数的短距离标度行为。利用密度泛函方法中的Calogero-Sutherland型相互作用，我们将基态能量移动与多体关联效应联系起来。对于激发态，模式的谐波频率$ω$的积分值，预测在一个维度上，与呼吸模式的频率$2ω$在两个维度。
英文摘要：
The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an $SO(2,1)$ symmetry in two dimensions. This facilitates an exact map from the interacting to the non-interacting system, both with and without a harmonic trap, and explains the short-distance scaling behavior of the wave-function. Taking advantage of the phenomenological Calogero-Sutherland-type interaction, motivated by the density functional approach, we connect the ground-state energy shift, to many-body correlation effect. For the excited states, modes at integral values of the harmonic frequency $ω$, are predicted in one dimension, in contrast to the breathing modes with frequency $2ω$ in two dimensions.
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