论文标题
量子晶体，kagome晶格和飞机隔板Fermion-Boson二元性
Quantum crystals, Kagome lattice and plane partitions fermion-boson duality
论文作者
论文摘要
在这项工作中，我们研究了三个空间维度的量子晶体熔化。使用六角形晶格中的二聚体的同等描述，我们将晶体融化的哈密顿量作为Kagome晶格中的占用问题。希尔伯特空间由平面隔板标记的状态跨越，并将其写为交错的整数分区的产物，我们为平面分区定义了Fermion-Boson二重性。最后，基于后者的结果，我们猜想量子哈密顿量的增长算子可以用仿射Yangian $ {\ cal y} [\ wideHat {\ Mathfrak {\ Mathfrak {gl}}（1）] $表示。
In this work, we study quantum crystal melting in three space dimensions. Using an equivalent description in terms of dimers in a hexagonal lattice, we recast the crystal melting Hamiltonian as an occupancy problem in a Kagome lattice. The Hilbert space is spanned by states labeled by plane partitions and writing them as a product of interlaced integer partitions, we define a fermion-boson duality for plane partitions. Finally, based upon the latter result we conjecture that the growth operators for the quantum Hamiltonian can be represented in terms of the affine Yangian ${\cal Y}[\widehat{\mathfrak{gl}}(1)]$.
