QUANTUM PHENOMENON QUANTUM PHENOMENON IN IN FM & AFM ANISOTROPIC FM & AFM ANISOTROPIC XXZ HEISENBERG CHAINS XXZ HEISENBERG CHAINS Global Renormalization-Group Global Renormalization-Group Analysis Analysis Ferromagnetic Excitation Spectrum Gap Ferromagnetic Excitation Spectrum Gap Antiferromagnetic Spin-Wave Stiffness Antiferromagnetic Spin-Wave Stiffness Ozan S. SARIYER [ Istanbul Tecnical University ] Ozan S. SARIYER [ Istanbul Tecnical University ] Prof. Dr. A. Nihat BERKER [ Koç Univ. - M.I.T. - Feza Gürsey Res. Inst. Prof. Dr. A. Nihat BERKER [ Koç Univ. - M.I.T. - Feza Gürsey Res. Inst. ] Dr. Michael HINCZEWSKI [ Feza Gürsey Res. Inst. ] Dr. Michael HINCZEWSKI [ Feza Gürsey Res. Inst. ]
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QUANTUM PHENOMENON IN FM & AFM ANISOTROPIC XXZ HEISENBERG CHAINS
QUANTUM PHENOMENON IN FM & AFM ANISOTROPIC XXZ HEISENBERG CHAINS. Global Renormalization-Group Analysis Ferromagnetic Excitation Spectrum Gap Antiferromagnetic Spin-Wave Stiffness Ozan S. SARIYER [ Istanbul Tecnical University ] - PowerPoint PPT Presentation
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QUANTUM QUANTUM PHENOMENON PHENOMENON ININ FM & FM & AFM ANISOTROPIC AFM ANISOTROPIC XXZ HEISENBERG XXZ HEISENBERG CHAINSCHAINSGlobal Renormalization-Group Global Renormalization-Group
2-dimensional XY model: Suzuki and Takano (1979,1981) 1,2,3-dimensional tJ electronic model: Falicov and Berker (1995) AF Heisenberg model on fractal (kagomé, squagome) lattices: Tomczak and Richter (1996,2003) 3-dimensional Hubbard electronic model: Hinczewski and Berker (2005)
M. Suzuki and H. Takano, Phys. Lett. A 69, 426 (1979). H. Takano and M. Suzuki, J. Stat. Phys. 26, 635 (1981). A. Falicov and A. N. Berker, Phys. Rev. B 51, 12458 (1995). P. Tomczak, Phys. Rev. B 53, R500 (1996). P. Tomczak and J. Richter, Phys. Rev. B 54, 9004 (1996). P. Tomczak and J. Richter, J. Phys. A 36, 5399 (2003). M. Hinczewski and A. N. Berker, Eur. Phys. J. B 48, 1 (2005).
Ozan S. SARIYER
Next: XXZ Model
XXZ MODELXXZ MODEL
Has been studied since the introduction of “spin” concept (Heisenberg, Bloch, Bethe, Hulthén 1930s) Still an actual problem in 2000s (Rojas et.al., Klümper, Bortz, Göhman... 2000s) Theory gained richness with Haldane’s studies (Haldane 1980s)
E. Lieb, T. Schultz and D. Mattis, Ann. of Phys. 16, 407 (1961). G. Kato, M. Shiroishi, M. Takahashi and K. Sakai, J. Phys. A 37,5097 (2004). N. Kitanine, J.M. Maillet, N.A. Slavnov and V. Terras, J. Stat. Mech. L09002 (2005). J. Sato, M. Shiroishi, and M. Takahashi, Nucl. Phys. B 729, 441 (2005). M. Takahashi, Thermodynamics of One-Dimensional Solvable Models, pgs. 41,56, 152-158, Cambridge University Press, Cambridge (1999).
Ozan S. SARIYER
Next: AFM T-dep. of Correlations
ANTIFERROMAGNETIC ANTIFERROMAGNETIC MODELMODELT-dependence of Correlations
M. Bortz ve F. Göhman, Eur. Phys. J. B 46, 399 (2005).
Ozan S. SARIYER
Next: AFM T-dep. of Spec. Heat
ANTIFERROMAGNETIC ANTIFERROMAGNETIC MODELMODELT-dependence of Specific Heat
A. Klümper, Int. of Qu.Chains: Th.and App.to the Spin-1/2 XXZ Ch., Lec.Not.in Phys.645, 349 (Springer, Berlin-Heidelberg 2004) J. C. Bonner and M. E. Fisher, Phys. Rev. 135, A640 (1964) C. Xi-Yao and G.F. Tuthill, Phys. Rev. B 32, 7280 (1985). R. Narayanan and R.R.P. Singh, Phys. Rev. B 42, 10305 (1990). K. Fabricius, A. Klümper and B.M. McCoy, Stat. Phys. on the Eve of the 21st Cent., 351 (World Scientific, Singapur 1999). A. Klümper, Lecture Notes in Phys. 645, 349 (Springer, Berlin-Heidelberg 2004)
W. J. Zhang, J. L. Shen, J. H. Xu and C. S. Ting, Phys. Rev. B 51, 2950 (1995). K. Fabricius, A. Klümper and B.M. McCoy, Stat. Phys. on the Eve of the 21st Cent., s.351 (World Scientific, Singapur 1999)
Ozan S. SARIYER
Next: AFM & FM Correlations
AFM AFM ANDAND FM FM CORRELATIONSCORRELATIONS
AFM FM
Ozan S. SARIYER
Next: FM T-dep. of Spec. Heat
FERROMAGNETIC MODELFERROMAGNETIC MODEL
T-dependence of Spec. Heat
S. Katsura, Phys. Rev. 127, 1508 (1962). J. C. Bonner and M. E. Fisher, Phys. Rev. 135, A640 (1964) C. Xi-Yao and G.F. Tuthill, Phys. Rev. B 32, 7280 (1985). W. J. Zhang, J. L. Shen, J. H. Xu and C. S. Ting, Phys. Rev. B 51, 2950 (1995). K. Fabricius, A. Klümper and B.M. McCoy, Stat. Phys. on the Eve of the 21st Cent., 351 (World Scientific, Singapur 1999).
Ozan S. SARIYER
Next: FM & AFM Spec. Heat
FM FM ANDAND AFM SPECIFIC AFM SPECIFIC HEATHEAT
FM AFM
Ozan S. SARIYER
Next: Excitation Spectrum Gap
FERROMAGNETIC MODELFERROMAGNETIC MODEL
Excitation Spectrum Gap and Exponent
F. D. M. Haldane, Phys. Rev. Lett. 45, 1358 (1980) F. D. M. Haldane, Phys. Rev. B 25, 4925 (1982) M. Takahashi, Thermodynamics of One-Dimensional Solvable Models, s. 152-158, Cambridge University Press, Cambridge (1999)
Ozan S. SARIYER
Next: Low-T Analysis
LOW-TEMPERATURE LOW-TEMPERATURE ANALYSISANALYSIS
M. Takahashi, Thermodynamics of One-Dimensional Solvable Models, s. 152-158, Cambridge University Press, Cambridge (1999)