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arXiv:cond-mat/0511469 · Physical Review B

Antiferromagnetic Heisenberg ladders in staggered magnetic field

Jize Zhao, Xiaoqun Wang, Tao Xiang, Zhao-Bin Su, Lu Yu, Jizhong Lou, Changfeng Chen

Published Jan 24, 2006• 7 citations
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Abstract

We study the low-energy excitations of the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg chain and $N$-leg $(N=2,3,4)$ ladders in a staggered magnetic field ${h}_{s}$. We show that ${h}_{s}$ induces gap and midgap states in all the cases and we will examine their field scaling behavior. A modified boundary scheme is devised to extract accurate bulk excitation behavior. The gap values converge rapidly as $N$ increases, leading to a field scaling exponent $\ensuremath{\gamma}=\frac{1}{2}$ for both the longitudinal and transverse gaps of the square lattice $(N\ensuremath{\rightarrow}\ensuremath{\infty})$. The midgap states induced by the boundary edge effects share the bulk gap scaling exponents but their overall scaling behavior in the large-$N$ limit needs further investigation.

DOI
10.1103/physrevb.73.012411

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We study low-energy excitations in antiferromagnetic Heisenberg chains with a staggered field which splits the spectrum into a longitudinal and a transverse branch. Bound states are found to exist inside the field induced gap in both branches. They originate from the edge effects and are inherent to spin-chain materials. The sine-Gordon scaling h(2/3)(s)[log(h(s)](1/6) (h(s), the staggered field) provides an accurate description for the gap and midgap energies in the transverse branch for S=1/2 and the midgap energies in both branches for S=3/2 over a wide range of magnetic field; however, it can fit other low-energy excitations only at much lower field. Moreover, the integer-spin S=1 chain displays scaling behavior that does not fit this scaling law. These results reveal intriguing features of magnetic excitations in spin-chain materials that deserve further investigation.
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We study the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg chain in both uniform and (perpendicular) staggered magnetic fields using the density-matrix renormalization-group method. This model has been shown earlier to describe the physics of the copper benzoate materials in magnetic field. In the present work, we extend the study to more general case for a systematic investigation of the field-induced gap and related properties of the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg chain. In particular, we explore the high magnetic field regime where interesting behaviors in the field-induced gap, magnetization, and spin correlation functions are found. Careful examination of the low energy properties and magnetization reveals interesting competing effects of the staggered and uniform fields. The incommensurate behavior in the spin correlation functions is demonstrated and discussed in detail. The present work reproduces earlier results in good agreement with experimental data on copper benzoate and predicts new interesting field-induced features at very high magnetic field.
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