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

Thiago Araujo, Domenico Orlando, Susanne Reffert

18/5/20 Published in : arXiv:2005.09103

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 meting 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, we show that the latter result implies that the growth operators for the quantum Hamiltonian can be represented in terms of operators in the affine Yangian of

\widehat{\mathfrak{gl}}(1)
Entire article

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Primordial magnetic helicity evolution with homogeneous magnetic field from inflation

Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions

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