DMCA
Asymmetric Diffusion And The Energy Gap Above The 111 Ground State Of The Quantum XXZ Model
| Citations: | 4 - 3 self |
BibTeX
@MISC{Caputo_asymmetricdiffusion,
author = {Pietro Caputo and Fabio Martinelli},
title = {Asymmetric Diffusion And The Energy Gap Above The 111 Ground State Of The Quantum XXZ Model},
year = {}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
We consider the anisotropic three dimensional XXZ Heisenberg ferromagnet in a cylinder with axis along the 111 direction and boundary conditions that induce ground states describing an interface orthogonal to the cylinder axis. Let L be the linear size of the basis of the cylinder. Because of the breaking of the continuous symmetry around the ^ z axis, the Goldstone theorem implies that the spectral gap above such ground states must tend to zero as L !1. In [3] it was proved that, by perturbing in a sub{cylinder with basis of linear size R L the interface ground state, it is possible to construct excited states whose energy gap shrinks as R . Here we prove that, uniformly in the height of the cylinder and in the location of the interface, the energy gap above the interface ground state is bounded from below by const.L . We prove the result by rst mapping the problem into an asymmetric simple exclusion process on Z then by adapting to the latter the recursive analysis to estimate from below the spectral gap of the associated Markov generator developed in [7]. Along the way we improve some bounds on the equivalence of ensembles already discussed in [3] and we establish an upper bound on the density of states close to the bottom of the spectrum. 2000 MSC: 82B10, 82B20, 60K35 Key words and phrases: XXZ model, quantum interface, asymmetric exclusion process, equivalence of ensembles, spectral gap. Date: June 25, 2001. 1.
Keyphrases
ground state energy gap quantum xxz model spectral gap asymmetric diffusion interface ground state linear size cylinder axis quantum interface key word energy gap shrink continuous symmetry associated markov generator excited state interface orthogonal upper bound boundary condition asymmetric simple exclusion process asymmetric exclusion process xxz model dimensional xxz heisenberg ferromagnet recursive analysis sub cylinder goldstone theorem implies
