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Scaling of excitations in dimerized and frustrated spin-1/2 chains

D. Controzzi·C. Degli Esposti Boschi·F. Ortolani·S. Pasini
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Abstract

We study the finite-size behavior of the low-lying excitations of spin-1/2 Heisenberg chains with dimerization and next-to-nearest neighbors interaction, J_2. The numerical analysis, performed using density-matrix renormalization group, confirms previous exact diagonalization results, and shows that, for different values of the dimerization parameter δ, the elementary triplet and singlet excitations present a clear scaling behavior in a wide range of \ell=L/ξ(where L is the length of the chain and ξis the correlation length). At J_2=J_2c, where no logarithmic corrections are present, we compare the numerical results with finite-size predictions for the sine-Gordon model obtained using Luscher's theory. For small δwe find a very good agreement for \ell > 4 or 7 depending on the excitation considered.

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D. Controzzi, C. Degli Esposti Boschi, F. Ortolani, S. Pasini. 2005-11-24. Scaling of excitations in dimerized and frustrated spin-1/2 chains. https://doi.org/10.1103/physrevb.72.172409

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