Energy Gap Estimates in XXZ Ferromagnets and Stochastic Particle Systems
2005, v.11, Issue 2, 189-210
This expository article is a survey of recent results [P. Caputo and F. Martinelli, Asymmetric diffusion and the energy gap above the 111 ground state of the quantum XXZ model. Commun. Math. Phys., 2002, v.226, 323-375. P. Caputo and F. Martinelli, Relaxation time of anisotropic simple exclusion processes and quantum Heisenberg models. Ann. Appl. Probab., 2003, v.13, no.2, 691-721] on the energy gap above the interface ground states of XXZ ferromagnets. Main ideas and techniques are reviewed with special emphasis on the equivalence between the quantum spin models and classical stochastic particle systems.
Keywords: simple exclusion,Heisenberg model,quantum interfaces,spectral gap