Closing of the Haldane gap in a spin-1 XXZ chain

다국어 초록 (Multilingual Abstract)

We study the energy gaps of a spin-1 XXZ model in one dimension. Using an infinite-size density matrix renormalization group (iDMRG) and a variational uniform matrix product state algorithm (vuMPS), we obtained the energy gaps ( E g ) as a function of anisotropy Δ . We found that the closing point of the energy gap changes as we increase the bond dimension. By scaling the energy gaps, we find the critical points for the Haldane-antiferromagnetic (H→AF) transition and the Haldane-XY (H→XY) phase transition. From the gap scaling formulae, E g(H → AF) = A(Δc1 − Δ)zν and E g(H → XY) = a exp(−bz'∕√Δ−Δc2) where z, z' are dynamical critical exponents, ν is a correlation length critical exponent, Δc1(2) is the critical point for each transition and A, a, and b are scaling parameters, we obtained information regarding the critical points and the scaling parameters.

참고문헌 (Reference)

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