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Communications in Mathematical Physics
, Volume 134, Issue 1, pp 127
Unitary dressing transformations and exponential decay below threshold for quantum spin systems. Parts I and II
 Claudio AlbaneseAffiliated withDepartment of Mathematics, University of California
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We consider a class of quantum spin systems defined on connected graphs of which the following HeisenbergXYmodel with a variable magnetic field gives an example: We treat first the case in whichh
_{
x
}=±1 for all sitesx and we introduce a unitary dressing transformation to control the spectrum for λ small. Then, we consider a situation in which h
_{
x
} can be less than one forx in a finite setL and prove exponential decay away fromL of dressed eigenfunctions with energy below the onequasiparticle threshold. If the ground state is separated by a finite gap from the rest of the spectrum, this result can be strengthened and one can compute a second unitary transformation that makes the ground state of compact support. Finally, a case in which the singular setL is of finite density, is considered. The main technical tools we use are decay estimates on dressed Green's functions and variational inequalities.
$$H_\lambda = \sum\limits_{x \in \mathbb{Z}^d } {h_x \sigma _x^{(3)} + \lambda } \sum\limits_{< x,y > \subset \mathbb{Z}^d } {(\sigma _x^{(1)} \sigma _y^{(1)} + \sigma _x^{(2)} \sigma _y^{(2)} )} .$$
 Title
 Unitary dressing transformations and exponential decay below threshold for quantum spin systems. Parts I and II
 Journal

Communications in Mathematical Physics
Volume 134, Issue 1 , pp 127
 Cover Date
 199011
 DOI
 10.1007/BF02102087
 Print ISSN
 00103616
 Online ISSN
 14320916
 Publisher
 SpringerVerlag
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 Authors

 Claudio Albanese ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of California, 900241555, Los Angeles, CA, USA