Determination of boundary scattering, magnon-magnon scattering, and the Haldane gap in Heisenberg spin chains
作者： Hiroshi Ueda , Koichi Kusakabe
DOI: 10.1103/PHYSREVB.84.054446
关键词: Physics 、 Scattering length 、 Coupling (probability) 、 Condensed matter physics 、 Quantum mechanics 、 Magnon 、 Antiferromagnetism 、 Density matrix renormalization group 、 Boundary (topology) 、 Scattering 、 Spin-½
摘要: Low-lying magnon dispersion in a $S=1$ Heisenberg antiferromagnetic (AF) chain is analyzed using the non-Abelian density-matrix-renormalization-group (DMRG) method. The scattering length ${a}_{\mathrm{b}}$ of boundary coupling and intermagnon $a$ are determined. found to exhibit characteristic diverging behavior at crossover point. In contrast, Haldane gap $\ensuremath{\Delta}$, velocity $v$, remain constant crossover. Our method allowed estimation $S=2$ AF be $\ensuremath{\Delta}=0.0891623(9)$ longer than correlation $\ensuremath{\xi}$.
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sci-hub.se 参考文章(28)
F.D.M. Haldane, Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model Physics Letters A. ,vol. 93, pp. 464- 468 ,(1983) , 10.1016/0375-9601(83)90631-X
F. D. M. Haldane, Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State Physical Review Letters. ,vol. 50, pp. 1153- 1156 ,(1983) , 10.1103/PHYSREVLETT.50.1153
Steven R. White, David A. Huse, Numerical renormalization-group study of low-lying eigenstates of the antiferromagnetic S=1 Heisenberg chain. Physical Review B. ,vol. 48, pp. 3844- 3852 ,(1993) , 10.1103/PHYSREVB.48.3844
Synge Todo, Kiyoshi Kato, Cluster algorithms for general-S quantum spin systems. Physical Review Letters. ,vol. 87, pp. 047203- 047203 ,(2001) , 10.1103/PHYSREVLETT.87.047203
Hiroki Nakano, Akira Terai, Reexamination of Finite-Lattice Extrapolation of Haldane Gaps Journal of the Physical Society of Japan. ,vol. 78, pp. 014003- ,(2009) , 10.1143/JPSJ.78.014003
Steven R. White, Ian Affleck, Spectral Function for the S=1 Heisenberg Antiferromagetic Chain Physical Review B. ,vol. 77, pp. 134437- ,(2008) , 10.1103/PHYSREVB.77.134437
Ian Affleck, The quantum hall effects, σ-models at Θ=π and quantum spin chains Nuclear Physics. ,vol. 257, pp. 397- 406 ,(1985) , 10.1016/0550-3213(85)90353-0
I Affleck, Quantum spin chains and the Haldane gap Journal of Physics: Condensed Matter. ,vol. 1, pp. 3047- 3072 ,(1989) , 10.1088/0953-8984/1/19/001
Tom Kennedy, Hal Tasaki, Hidden Z 2 × Z 2 symmetry breaking in Haldane-gap antiferromagnets Physical Review B. ,vol. 45, pp. 304- 307 ,(1992) , 10.1103/PHYSREVB.45.304
Steven R. White, Density matrix formulation for quantum renormalization groups Physical Review Letters. ,vol. 69, pp. 2863- 2866 ,(1992) , 10.1103/PHYSREVLETT.69.2863