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Upper and Lower Bounds on the Partition Function of the Hofstadter Model | | Alexander Moroz
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14 May 1996 | | Journal: | Mod.Phys.Lett. B10 (1996) 409-416 | | Abstract: | Using unitary equivalence of magnetic translation operators, explicit upper and lower convex bounds on the partition function of the Hofstadter model are given for any rational ``flux" and any value of Bloch momenta. These bounds (i) generalize straightforwardly to the case of a general asymmetric hopping and to the case of hopping of the form $t_{jn}(S_j^n+S_j^{-n})$ with $n$ arbitrary integer larger than or equal $2$, and (ii) allow to derive bounds on the derivatives of the partition function. | | Source: | arXiv, cond-mat/9601083 | | Services: | Forum | Review | PDF | Favorites | |
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