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Equivalence between XY and dimerized models

Lorenzo Campos Venuti and Marco Roncaglia
Phys. Rev. A 81, 060101(R) – Published 14 June 2010

Abstract

The spin-1/2 chain with XY anisotropic coupling in the plane and the 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 XY chain can be mapped onto an XX model. This result has potential application in the study of disordered systems.

  • Received 17 February 2010

DOI:https://doi.org/10.1103/PhysRevA.81.060101

©2010 American Physical Society

Authors & Affiliations

Lorenzo Campos Venuti1 and Marco Roncaglia2,1

  • 1Institute for Scientific Interchange, ISI Foundation, Viale S. Severo 65, I-10133 Torino, Italy
  • 2Dipartimento di Matematica e Informatica, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy

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Issue

Vol. 81, Iss. 6 — June 2010

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