Letters in Mathematical Physics

, Volume 77, Issue 1, pp 11–20 | Cite as

Out of Equilibrium Correlations in the XY Chain

Article

Abstract

We study the transversal spin–spin correlations in the non-equilibrium steady state of the XY chain constructed by coupling a finite cutout of the chain to the two infinite parts to its left and right acting as thermal reservoirs at different temperatures. We prove that the spatial decay of these correlations is at least exponentially fast.

Keywords

non-equilibrium steady state XY chain correlations Toeplitz operators 

Mathematics Subject Classification (2000)

46L60 47B35 82C10 82C23 

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References

  1. 1.
    Araki H. (1971). On quasifree states of CAR and Bogoliubov automorphisms. Publ. RIMS. Kyoto. Univ. 6:385–442MathSciNetCrossRefGoogle Scholar
  2. 2.
    Araki H. (1984). On the XY-model on two-sided infinite chain. Publ. RIMS. Kyoto. Univ. 20:277–296MathSciNetMATHGoogle Scholar
  3. 3.
    Araki H., Ho T.G. (2000). Asymptotic time evolution of a partitioned infinite two-sided isotropic XY-chain. Proc. Steklov Inst. Math. 228:191–204MathSciNetGoogle Scholar
  4. 4.
    Aschbacher W.H., Pillet C.-A. (2003). Non-equilibrium steady states of the XY chain. J. Stat. Phys. 112:1153–1175CrossRefMathSciNetMATHGoogle Scholar
  5. 5.
    Aschbacher, W.H., Jakšić, V., Pautrat, Y., Pillet, C.-A.: Topics in non-equilibrium quantum statistical mechanics. Lecture notes in mathematics. Springer, Berlin New York (in Press)Google Scholar
  6. 6.
    Barouch E., McCoy B.M. (1971). Statistical mechanics of the XY model. II. Spin-correlation functions. Phys. Rev. A. 3:786–804CrossRefADSGoogle Scholar
  7. 7.
    Böttcher A., Silbermann B. (1990). Analysis of Toeplitz operators. Springer, Berlin Heidelberg New YorkMATHGoogle Scholar
  8. 8.
    Böttcher A., Silbermann B. (1999). Introduction to large truncated Toeplitz matrices. Springer, Berlin Heidelberg New YorkMATHGoogle Scholar
  9. 9.
    Bratteli O., Robinson D.W. (1997). Operator algebras and quantum statistical mechanics vol 2. Springer, Berlin Heidelberg New YorkGoogle Scholar
  10. 10.
    Jakšić V., Pillet C.-A. (2002). Mathematical theory of non-equilibrium quantum statistical mechanics. J. Stat. Phys. 108:787–829CrossRefMATHGoogle Scholar
  11. 11.
    Lieb E., Schultz T., Mattis D. (1961). Two soluble models of an antiferromagnetic chain. Ann. Phys. 16:407–466CrossRefADSMathSciNetMATHGoogle Scholar
  12. 12.
    McCoy B. (1968). Spin correlation functions of the XY model. Phys. Rev. 173:531–541CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    Ruelle D. (2001). Entropy production in quantum spin systems. Comm. Math. Phys. 224:3–16CrossRefADSMathSciNetMATHGoogle Scholar
  14. 14.
    Sologubenko, A.V., Giannò, K., Ott, H.R., Vietkine, A., Revcolevschi, A.: Heat transport by lattice and spin excitations in the spin-chain compounds SrCuO2 and Sr2CuO3. Phys. Rev. B. 64, 054412 1–054412 11 (2001)Google Scholar
  15. 15.
    Sologubenko A.V., Felder E., Giannò K., Ott H.R., Vietkine A., Revcolevschi A. (2000). Thermal conductivity and specific heat of the linear chain cuprate Sr2CuO3: evidence for the thermal transport via spinons. Phys. Rev. B. 62:R6108–R6111CrossRefADSGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Zentrum MathematikTechnische Universität München, M5GarchingGermany
  2. 2.Centre de Physique ThéoriqueLuminyMarseilleFrance
  3. 3.Département de MathématiquesUniversité du Sud Toulon-VarLa GardeFrance

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