Quantum crystals, Kagome lattice and plane partitions fermion-boson duality

Abstract

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 $\mathcal{Y}[\widehat{\mathfrak{gl}}(1)]$.

13 pages, 13 figures; v2: published version

References in corpus (5)

• Topological Order and Conformal Quantum Critical Points
• Relating Field Theories via Stochastic Quantization
• Crystal Melting and Black Holes
• The uses of random partitions
• Quantum Crystals and Spin Chains

Cited by in corpus (3)

• Interface dynamics in the two-dimensional quantum Ising model
• Localization and melting of interfaces in the two-dimensional quantum Ising model
• Towards Yang-Baxter integrability of quantum crystal melting: From Kagome lattice to vertex models