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arXiv:cond-mat/0511467 · Physical Review Letters

Midgap States in Antiferromagnetic Heisenberg Chains with a Staggered Field

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

Published Jun 3, 2005• 24 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.94.217207

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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) (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.
We study the low-energy excitations of the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg chain and NNN-leg (N=2,3,4)(N=2,3,4)(N=2,3,4) ladders in a staggered magnetic field hs{h}_{s}hs​. We show that hs{h}_{s}hs​ 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 NNN 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-NNN limit needs further investigation.
A recent study [J. Lou, et al., Phys. Rev. Lett. 94, 217207 (2005)] reveals that topological edge effects induce bound midgap states in antiferromagnetic Heisenberg chains with a staggered magnetic field. We report density matrix renormalization group calculations that examine the effects of high magnetic field on the gap and midgap states and the range of validity of the field theory prediction on their scaling behavior. We also investigate the effects of the site parity (i.e., even or odd number of sites in the chain), the dilution of the spin chain by dopant atoms, and the uniform magnetic field on the emergence and evolution of the midgap states. The results provide useful insights into the behavior of the edge excitations in spin chain materials, which should facilitate the comparison between theory and experiment and stimulate further investigations.
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.
Abstract A spin-1/2 Heisenberg antiferromagnetic chain is one of the most important paradigmatic models in quantum magnetism. Its ground state is a spin singlet, while the excitation spectrum is formed by gapless fractional excitations, spinons. The presence of alternating g-tensors and/or the staggered Dzyaloshinskii-Moriya interaction results in opening the energy gap Δ∝H2/3\varDelta \propto H^{2/3}Δ∝H2/3 Δ ∝ H 2 / 3 , once the magnetic field H is applied. A fairly good understanding of this phenomenon was achieved in the framework of the sine-Gordon quantum-field theory, taking into account the effective transverse staggered field induced by the applied uniform field. The theory predicts solitons and antisolitons as elementary excitations, as well as their bound states, breathers. Here, I review recent high-field electron spin resonance spectroscopy studies of such systems, focusing on peculiarities of their spin dynamics in the sine-Gordon regime and beyond.
This article is a review of the recent achievements in experimental studies of magnetic excitations in the copper pyrimidine dinitrate [PM–Cu(NO3)2(H2O)2]n (PM = pyrimidine), an S = 1/2 antiferromagnetic chain material with an alternating g-tensor and the Dzyaloshinskii–Moriya interaction, by means of high-field electron spin resonance (ESR). Due to this alternation, in the 1D critical regime this material exhibits a field-induced gap. The excitation spectrum is formed by solitons and their bound states, breathers, and can be effectively described using the sine-Gordon model. With increasing temperature, the soliton-breather regime can be suppressed, resulting in a substantial evolution of ESR parameters. These changes can be described using a new theoretical concept recently proposed for S = 1/2 AF chains with a staggered transverse field. High magnetic field induces a transition into the spin-polarized state with the excitation spectrum formed by magnons. Nonmonotonous behavior of the field-induced gap is observed in vicinity of the saturation field. Experimental data are compared with results of existing theoretical approaches, revealing excellent agreement with predictions.
The infinite Heisenberg XXZ spin-12\frac{1}{2}21​ chain in the gapped antiferromagnetic regime has two degenerate vacua and kink topological excitations (which are also called spinons) interpolating between these vacua as elementary excitations. Application of an arbitrary weak staggered longitudinal magnetic field hhh induces a long-range attractive potential between two adjacent spinons leading to their confinement into ``meson'' bound states. Exploiting the integrability of the XXZ model in the deconfined phase h=0h=0h=0, we perform perturbative calculations of the energy spectra of the two-spinon bound states in the weak confinement regime at $h\ensuremath{\rightarrow}+0$, using the strength of the staggered magnetic field hhh as a small parameter. Both transverse and longitudinal dynamical structure factors of the local spin operators are calculated as well in the two-spinon approximation in the weak confinement regime to the leading order in hhh.