Quantum renormalization effect in one-dimensional Heisenberg antiferromagnets

晋一伊藤, Shinichi Itoh, Tetsuya YOKOO, Shin-ichiro Yano, Daichi Kawana, 秀数田中, HIDEKAZU TANAKA, Y. Endoh

Published Jul 1, 2012• 0 citations

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Published Jul 1, 2012• 0 citations

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We perform a real-space renormalization-group analysis for the two-dimensional antiferromagnetic Heisenberg model. We first derive an effective model, described by the Hamiltonian: H=J ${\mathcal{J}}_{\mathit{j}=1}^{\mathit{L}}$ S(j)\ensuremath{\cdot}S(j+1)+ ${\mathcal{J}}_{\mathit{j}=1}^{\mathit{L}}$ (-1 ${)}^{\mathit{j}}$ \ensuremath{\Vert}J(j)\ensuremath{\Vert}S(0)\ensuremath{\cdot}S(j), where S(0) represents a single spin located in the center of the ring. We show that the renormalized coupling constants \ensuremath{\Vert}J(j)\ensuremath{\Vert} tend to nonzero values as one increases the block size by successive renormalization. Using analytic and numerical arguments, we establish the existence of antiferromagnetic long-range order in the effective model and hence, in the original Heisenberg model. We compare our results with those obtained from perturbation theory, spin-wave theory, and exact-diagonalization calculations.We perform a real-space renormalization-group analysis for the two-dimensional antiferromagnetic Heisenberg model. We first derive an effective model, described by the Hamiltonian: H=J ${\mathcal{J}}_{\mathit{j}=1}^{\mathit{L}}$ S(j)\ensuremath{\cdot}S(j+1)+ ${\mathcal{J}}_{\mathit{j}=1}^{\mathit{L}}$(-1${)}^{\mathit{j}}$\ensuremath{\Vert}J(j)\ensuremath{\Vert}S(0)\ensuremath{\cdot}S(j), where S(0) represents a single spin located in the center of the ring. We show that the renormalized coupling constants \ensuremath{\Vert}J(j)\ensuremath{\Vert} tend to nonzero values as one increases the block size by successive renormalization. Using analytic and numerical arguments, we establish the existence of antiferromagnetic long-range order in the effective model and hence, in the original Heisenberg model. We compare our results with those obtained from perturbation theory, spin-wave theory, and exact-diagonalization calculations.

Physical review. B, Condensed matterNov 1, 19942 citations

We perform a real-space renormalization-group analysis for the two-dimensional antiferromagnetic Heisenberg model. We first derive an effective model, described by the Hamiltonian: H=J

{\mathcal{J}}_{\mathit{j}=1}^{\mathit{L}}

S(j)\ensuremath{\cdot}S(j+1)+

{\mathcal{J}}_{\mathit{j}=1}^{\mathit{L}}

(-1

{)}^{\mathit{j}}

\ensuremath{\Vert}J(j)\ensuremath{\Vert}S(0)\ensuremath{\cdot}S(j), where S(0) represents a single spin located in the center of the ring. We show that the renormalized coupling constants \ensuremath{\Vert}J(j)\ensuremath{\Vert} tend to nonzero values as one increases the block size by successive renormalization. Using analytic and numerical arguments, we establish the existence of antiferromagnetic long-range order in the effective model and hence, in the original Heisenberg model. We compare our results with those obtained from perturbation theory, spin-wave theory, and exact-diagonalization calculations.