Quantum behavior at mesoscopic length scales is of significant interest, both from a fundamental-physics standpoint, as well as in the context of technological advances. In this light, the description of collective variables comprising large numbers of atoms, but nevertheless displaying non-classical behavior, is a fundamental problem. Here, we show that an effective-Hamiltonian approach for such variables, as has been applied to describe the quantum behavior of coupled qubit/oscillator systems, can also be very useful in understanding intrinsic behavior of quantum materials. We consider lattice dislocations – naturally occurring mesoscopic line defects in crystals – in the prototypical bosonic quantum crystal, solid ⁴He. For this purpose, we map fully atomistic quantum simulations onto effective one-dimensional Hamiltonians in which the collective dislocation-position variables are represented as interacting, massive quantum particles. The results provide quantitative understanding of several experimental observations in solid ⁴He.

无论是从基础物理学的角度还是在技术进步的背景下，介观长度尺度的量子行为都具有重要意义。从这个角度来看，描述包含大量原子但仍显示出非经典行为的集体变量是一个基本问题。在这里，我们展示了针对此类变量的有效哈密顿方法，如已应用于描述耦合量子位/振荡器系统的量子行为，对于理解量子材料的本征行为也非常有用。我们考虑晶格位错——晶体中自然发生的介观线缺陷——在原型玻色子量子晶体中，固体⁴他。为此，我们将完全原子的量子模拟映射到有效的一维哈密顿量上，其中集体位错位置变量表示为相互作用的大质量量子粒子。结果提供了对固体⁴ He 中几个实验观察结果的定量理解。