Hummel Quirin, Urbina Juan Diego, Richter Klaus
Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany.
Phys Rev Lett. 2019 Jun 21;122(24):240601. doi: 10.1103/PhysRevLett.122.240601.
Because of the vast growth of the many-body level density with excitation energy, its smoothed form is of central relevance for spectral and thermodynamic properties of interacting quantum systems. We compute the cumulative of this level density for confined one-dimensional continuous systems with repulsive short-range interactions. We show that the crossover from an ideal Bose gas to the strongly correlated, fermionized gas, i.e., partial fermionization, exhibits universal behavior: Systems with very few and up to many particles share the same underlying spectral features. In our derivation we supplement quantum cluster expansions with short-time dynamical information. Our nonperturbative analytical results are in excellent agreement with numerics for systems of experimental relevance in cold atom physics, such as interacting bosons on a ring (Lieb-Liniger model) or subject to harmonic confinement. Our method provides predictions for excitation spectra that enable access to finite-temperature thermodynamics in large parameter ranges.
由于多体能级密度随激发能的巨大增长，其平滑形式对于相互作用量子系统的光谱和热力学性质至关重要。我们计算了具有排斥性短程相互作用的受限一维连续系统的这种能级密度的累积量。我们表明，从理想玻色气体到强关联的费米化气体的转变，即部分费米化，表现出普遍行为：粒子数很少到很多的系统都具有相同的潜在光谱特征。在我们的推导中，我们用短时间动力学信息补充了量子团簇展开。我们的非微扰分析结果与冷原子物理中具有实验相关性的系统的数值结果非常吻合，例如环上的相互作用玻色子（李 - 林格模型）或受到谐波限制的情况。我们的方法为激发光谱提供了预测，从而能够在大参数范围内获取有限温度的热力学信息。
