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RESEARCH PRODUCT
Equivalence betweenXYand dimerized models
Lorenzo Campos VenutiMarco RoncagliaMarco Roncagliasubject
PhysicsCouplingQuantum PhysicsAngular momentumStrongly Correlated Electrons (cond-mat.str-el)Statistics::ApplicationsIsotropyFinite systemFOS: Physical sciencesParity (physics)01 natural sciencesUnitary stateAtomic and Molecular Physics and Optics010305 fluids & plasmasCondensed Matter - Other Condensed MatterCondensed Matter - Strongly Correlated ElectronsQuantum mechanics0103 physical sciencesBoundary value problemQuantum Physics (quant-ph)010306 general physicsAnisotropyOther Condensed Matter (cond-mat.other)Mathematical physicsdescription
The spin-$1/2$ chain with $\mathit{XY}$ anisotropic coupling in the plane and the $\mathit{XX}$ isotropic dimerized chain are shown to be equivalent in the bulk. For finite systems, we prove that the equivalence is exact in given parity sectors, after taking care of the precise boundary conditions. The proof is given constructively by finding unitary transformations that map the models onto each other. Moreover, we considerably generalized our mapping and showed that even in the case of fully site-dependent couplings the $\mathit{XY}$ chain can be mapped onto an $\mathit{XX}$ model. This result has potential application in the study of disordered systems.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-06-14 | Physical Review A |