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Heat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D regime

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Abstract

We study the anisotropic quantum Heisenberg antiferromagnet for spin-1/2 that interpolates smoothly between the one-dimensional (1D) and the two-dimensional (2D) limits. Using the spin Hartree-Fock approach we construct a quantitative theory of heat capacity in the quasi-1D regime with a finite coupling between spin chains. This theory reproduces closely the exact result of Bethe Ansatz in the 1D limit and does not produces any spurious phase transitions for any anisotropy in the quasi-1D regime at finite temperatures in agreement with the Mermin-Wagner theorem. We study the static spin-spin correlation function in order to analyse the interplay of lattice geometry and anisotropy in these systems. We compare the square and triangular lattice. For the latter we find that there is a quantum transition point at an intermediate anisotropy of ~0.6. This quantum phase transition establishes that the quasi-1D regime extends upto a particular point in this geometry. For the square lattice the change from the 1D to 2D occurs smoothly as a function of anisotropy, i.e. it is of the crossover type. Comparing the newly developed theory to the available experimental data on the heat capacity of Cs2CuBr4 and Cs2CuCl4 we extract the microscopic constants of the exchange interaction that previously could only be measured using inelastic neutron scattering in high magnetic fields.

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References

  1. Y. Trudeau, M. Poirier, A. Caillé, Phys. Rev. B 46, 169 (1992)

    Article  ADS  Google Scholar 

  2. R. Coldea, D.A. Tennant, Z. Tylczynski, Phys. Rev. B 68, 134424 (2003)

    Article  ADS  Google Scholar 

  3. A. Sytcheva, O. Chiatti, J. Wosnitza, S. Zherlitsyn, A.A. Zvyagin, R. Coldea, Z. Tylczynski, Phys. Rev. B 80, 224414 (2009)

    Article  ADS  Google Scholar 

  4. T. Ono, H. Tanaka, H. Aruga Katori, F. Ishikawa, H. Mitamura, T. Goto, Phys. Rev. B 67, 104431 (2003)

    Article  ADS  Google Scholar 

  5. M. Gaudin,The Bethe Wavefunction (Cambridge University Press, Cambridge, 2014)

  6. F.J. Dyson, E.H. Lieb, B. Simon, J. Stat. Phys. 18, 335 (1978)

    Article  ADS  Google Scholar 

  7. T. Kennedy, E.H. Lieb, B.S. Shastry, J. Stat. Phys. 53, 1019 (1988)

    Article  ADS  Google Scholar 

  8. M. Takahashi, Phys. Rev. Lett. 58, 168 (1987)

    Article  ADS  Google Scholar 

  9. D.P. Arovas, A. Auerbach, Phys. Rev. Lett. 61, 617 (1988)

    Article  ADS  Google Scholar 

  10. D.P. Arovas, A. Auerbach, Phys. Rev. B 38, 316 (1989)

    Article  ADS  Google Scholar 

  11. M. Takahashi, Prog. Theor. Phys. 46, 401 (1971)

    Article  ADS  Google Scholar 

  12. M. Gaudin, Phys. Rev. Lett. 26, 1301 (1971)

    Article  ADS  Google Scholar 

  13. N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17, 1133 (1966)

    Article  ADS  Google Scholar 

  14. P.W. Anderson, G. Baskaran, Z. Zou, T. Hsu, Phys. Rev. Lett. 58, 2790 (1987)

    Article  ADS  Google Scholar 

  15. S. Liang, B. Doucot, P.W. Anderson, Phys. Rev. Lett. 61, 365 (1988)

    Article  ADS  Google Scholar 

  16. Y.R. Wang, Phys. Rev. B 45, 12604 (1992)

    Article  ADS  Google Scholar 

  17. B. Bernu, G. Misguich, Phys. Rev. B 63, 134409 (2001)

    Article  ADS  Google Scholar 

  18. A. Werth, P. Kopietz, O. Tsyplyatyev, Phys. Rev. B 97, 180403 (R) (2018)

    Article  ADS  Google Scholar 

  19. R. Coldea, D.A. Tennant, K. Habicht, P. Smeibidl, C. Wolters, Z. Tylczynski, Phys. Rev. Lett. 88, 137203 (2002)

    Article  ADS  Google Scholar 

  20. L. Balents, Nature (London) 464, 199 (2010)

    Article  ADS  Google Scholar 

  21. O. Tsyplyatyev, A.J. Schofield, Phys. Rev. B 90, 014309 (2014)

    Article  ADS  Google Scholar 

  22. O. Tsyplyatyev, A.J. Schofield, Y. Jin, M. Moreno, W.K. Tan, C.J.B. Ford, J.P. Griffiths, I. Farrer, G.A.C. Jones, D.A. Ritchie, Phys. Rev. Lett. 114, 196401 (2015)

    Article  ADS  Google Scholar 

  23. O. Tsyplyatyev, A.J. Schofield, Y. Jin, M. Moreno, W.K. Tan, A.S. Anirban, C.J.B. Ford, J.P. Griffiths, I. Farrer, G.A.C. Jones, D.A. Ritchie, Phys. Rev. B 93, 075147 (2016)

    Article  ADS  Google Scholar 

  24. M. Moreno, C.J.B. Ford, Y. Jin, J.P. Griffiths, I. Farrer, G.A.C. Jones, D.A. Ritchie, O. Tsyplyatyev, A.J. Schofield, Nat. Commun. 7, 12784 (2016)

    Article  ADS  Google Scholar 

  25. H. Bethe, Z. Phys. 71, 205 (1931)

    Article  ADS  Google Scholar 

  26. M. Takahashi, Prog. Theor. Phys. 50, 1519 (1973)

    Article  ADS  Google Scholar 

  27. A. Klümper, Z. Phys. B 91, 507 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  28. J. Krieg, P. Kopietz, Phys. Rev. B 99, 060403(R) (2019)

    Article  ADS  Google Scholar 

  29. M. Kohno, O.A. Starykh, L. Balents, Nat. Phys. 3, 790 (2007)

    Article  Google Scholar 

  30. S. Yunoki, S. Sorella, Phys. Rev. B 74, 014408 (2006)

    Article  ADS  Google Scholar 

  31. Y. Hayashi, M. Ogata, J. Phys. Soc. Jpn. 76, 053705 (2007)

    Article  ADS  Google Scholar 

  32. R. Orbach, Phys. Rev. 112, 309 (1958)

    Article  ADS  Google Scholar 

  33. B. Bernu, P. Lecheminant, C. Lhuillier, L. Pierre, Phys. Rev. B 50, 10048 (1994)

    Article  ADS  Google Scholar 

  34. D. Heidarian, S. Sorella, F. Becca, Phys. Rev. B 80, 012404 (2009)

    Article  ADS  Google Scholar 

  35. A.W. Sandvik, Phys. Rev. B 56, 11678 (1997)

    Article  ADS  Google Scholar 

  36. T. Radu, H. Wilhelm, V. Yushankhai, D. Kovrizhin, R. Coldea, Z. Tylczynski, T. Lühmann, F. Steglich, Phys. Rev. Lett. 95, 127202 (2005)

    Article  ADS  Google Scholar 

  37. U. Tutsch, O. Tsyplyatyev, M. Kuhnt, L. Postulka, B. Wolf, P.T. Cong, F. Ritter, C. Krellner, W. Aßmus, B. Schmidt, P. Thalmeier, P. Kopietz, M. Lang, Phys. Rev. Lett. 123, 147202 (2019)

    Article  ADS  Google Scholar 

  38. https://onlinelibrary.wiley.com/toc/15213951/2019/256/9

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Frankfurt, Max-von-Laue Strasse 1, 60438, Frankfurt, Germany

    Roman Smit, Peter Kopietz & Oleksandr Tsyplyatyev

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  1. Roman Smit
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  2. Peter Kopietz
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  3. Oleksandr Tsyplyatyev
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Correspondence to Oleksandr Tsyplyatyev.

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Smit, R., Kopietz, P. & Tsyplyatyev, O. Heat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D regime. Eur. Phys. J. B 92, 252 (2019). https://doi.org/10.1140/epjb/e2019-100387-9

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