论文标题
耗尽纤毛链的耗尽
Depletion in fermionic chains with inhomogeneous hoppings
论文作者
论文摘要
在半填充时具有不均匀跳的自由花链的基态可以在静态弯曲的时空上映射到狄拉克真空中，该时空由于粒子孔对称性而恰好呈现均匀的职业。然而，我们远没有半填充，我们观察到密度调制和耗竭效应。该系统可以由1DSchrödinger方程在不同的静态时空中描述，其有效潜力可以解释耗尽的区域。我们为单粒子模式和与不同跳跃模式和填充分数相关的密度分布提供了半经典表达式。此外，我们表明，可以通过与跳跃成比例的化学势来补偿所有填充分数的耗竭效应。有趣的是，如果我们引入与跳跃强度相反的化学电位，即使基态不同于原始链，我们就可以在均匀链上获得完全相同的密度曲线。
The ground state of a free-fermionic chain with inhomogeneous hoppings at half-filling can be mapped into the Dirac vacuum on a static curved space-time, which presents exactly homogeneous occupations due to particle-hole symmetry. Yet, far from half-filling we observe density modulations and depletion effects. The system can be described by a 1D Schrödinger equation on a different static space-time, with an effective potential which accounts for the depleted regions. We provide a semiclassical expression for the single-particle modes and the density profiles associated to different hopping patterns and filling fractions. Moreover, we show that the depletion effects can be compensated for all filling fractions by adding a chemical potential proportional to the hoppings. Interestingly, we can obtain exactly the same density profiles on a homogeneous chain if we introduce a chemical potential which is inverse to the hopping intensities, even though the ground state is different from the original one.
