Quantum Crystals and Spin Chains

Details Quantum Crystals and Spin Chains Quantum Crystals and Spin Chains

2008-03-13

arxiv.org/abs/0803.1927v2

Nucl.Phys.B811:463-490,2009

Physics

Condensed Matter

Statistical Mechanics

34 pages, 26 pictures

Scientific paper

10.1016/j.nuclphysb.2008.11.027

In this note, we discuss the quantum version of the melting crystal corner in one, two, and three dimensions, generalizing the treatment for the quantum dimer model. Using a mapping to spin chains we find that the two--dimensional case (growth of random partitions) is integrable and leads directly to the Hamiltonian of the Heisenberg XXZ ferromagnet. The three--dimensional case of the melting crystal corner is described in terms of a system of coupled XXZ spin chains. We give a conjecture for its mass gap and analyze the system numerically.

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