Quantum Crystals and Spin Chains

Abstract

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.

34 pages, 26 pictures

References in corpus (6)

• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Quantum Foam and Topological Strings
• From quantum mechanics to classical statistical physics: generalized Rokhsar-Kivelson Hamiltonians and the "Stochastic Matrix Form" decomposition
• Ground states of the infinite q-deformed Heisenberg ferromagnet
• Droplet Excitations for the Spin-1/2 XXZ Chain with Kink Boundary Conditions
• Some properties for the low-lying spectrum of the ferromagnetic, quantum XXZ spin system

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• On the density matrix for the kink ground state of higher spin XXZ chain