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arXiv:cond-mat/9510069 · Journal of Physics A Mathematical and General

Critical properties of theXXZchain in an external staggered magnetic field

Kiyomi Okamoto, Kiyohide Nomura

Published May 7, 1996• 15 citations
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Abstract

We comment on the recent work of Alcaraz and Malvezzi on the critical properties of the chain in staggered magnetic field. The method of determining the phase boundary from the finite-size numerical data is also discussed.
DOI
10.1088/0305-4470/29/9/036

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The phase diagram of the XXZ chain is calculated under the influence of homogeneous and staggered magnetic fields. The model has a rich phase structure with three types of phases. A fully ferromagnetic phase, an antiferromagnetic phase and a massless phase with partial ferromagnetic and antiferromagnetic order. This massless phase's critical fluctuations are governed by a conformal field theory with central charge c=1. When the sigma z -anisotropy Delta is zero the model is exactly integrable through a Jordan-Wigner fermionization and our results are analytic. For Delta not=0 our analysis is done numerically using lattice sizes up to M=20. Our results show that for -1<or= Delta < square root (2/2) the staggered magnetic field perturbation is relevant, whereas for square root (2/2)< Delta <or=1 it is irrelevant. In the region of relevant perturbations, we show that the massive continuum field theory associated with the model, has the same mass spectrum as the sine-Gordon model.
The ground states of the S=12S=\frac{1}{2}S=21​ Heisenberg chain with the nearest-neighbor and the next-nearest-neighbor antiferromagnetic couplings are numerically investigated in a staggered magnetic field. While the staggered magnetic field may induce the N\'eel-type excitation gap, and it is characterized by the Gaussian fixed point in the spin-fluid region, the crossover to the behavior controlled by the Ising fixed point is expected to be observed for the spontaneously dimerized state at finite field. Treating a low-lying excitation gap by the phenomenological renormalization-group method, we numerically determine the massless flow connecting the Gaussian and Ising fixed points. Further, to check the criticalities, we perform the finite-size-scaling analysis of the excitation gap.
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