Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9803393 · Physical Review Letters

Universal Behavior of One-Dimensional Gapped Antiferromagnets in a Staggered Magnetic Field

Sergei Maslov, A. Zheludev

Published Jun 29, 1998• 41 citations
arXivHTMLPDF

Abstract

We study the properties of one-dimensional gapped Heisenberg antiferromagnets in the presence of a strong staggered magnetic field. For these systems we predict a universal form for the staggered magnetization curve. This function, as well as the effect the staggered field has on the energy gaps in longitudinal and transversal excitation spectra, is determined from the universal form of the effective potential in $O(3)$-symmetric $(1+1)$-dimensional field theory. Our theoretical findings are in excellent agreement with recent neutron scattering data on ${R}_{2}{\mathrm{BaNiO}}_{5}$ ( $R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}$ magnetic rare earth) linear-chain mixed spin antiferromagnets.

DOI
10.1103/physrevlett.80.5786

Related papers

Heisenberg spin-1 chain in a staggered magnetic field: A density-matrix-renormalization-group study

Jizhong Lou, Xi Dai, Shaojin Qin +2 more

Using the density-matrix-renormalization-group technique, we calculate numerically the low-energy excitation spectrum and magnetization curve of the spin-1 antiferromagnetic chain in a staggered magnetic field, which is expected to describe the physics of the ${R}_{2}{\mathrm{BaNiO}}_{5} (R\ensuremath{\ne}Y)$ family below the N\'eel temperature of the magnetic rare-earth (R) sublattice. These results are valid in the entire range of the staggered field, and agree with those given by the nonlinear $\ensuremath{\sigma}$ model study for small fields, but differ from the latter for large fields. They are consistent with the available experimental data. The correlation functions for this model are also calculated. The transverse correlations display the anticipated exponential decay with shorter correlation length, while the longitudinal correlations show explicitly the induced staggered magnetization.

arXiv:cond-mat/9904035•Physical review. B, Condensed matter•Jul 1, 1999•28 citations

Antiferromagnetic Heisenberg ladders in staggered magnetic field

Jize Zhao, Xiaoqun Wang, Tao Xiang +4 more

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.

arXiv:cond-mat/0511469•Physical Review B•Jan 24, 2006•7 citations

Midgap States in Antiferromagnetic Heisenberg Chains with a Staggered Field

Jizhong Lou, Changfeng Chen, Jize Zhao +4 more

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.

arXiv:cond-mat/0511467•Physical Review Letters•Jun 3, 2005•24 citations

Field-induced gap in the spin- 12 antiferromagnetic Heisenberg chain: A density-matrix renormalization-group study

Jizhong Lou, Shaojin Qin, Changfeng Chen +2 more

We study the spin-$\frac{1}{2}$ 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-$\frac{1}{2}$ 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.

arXiv:cond-mat/0204489•Physical review. B, Condensed matter•Jan 17, 2002•21 citations

Spin-1 antiferromagnetic Heisenberg chains in an external staggered field

Elisa Ercolessi, G. Morandi, P. Pieri +1 more

We present in this paper a nonlinear \ensuremath{\sigma}-model analysis of a spin-1 antiferromagnetic Heisenberg chain in an external commensurate staggered magnetic field. After rediscussing briefly and extending previous results for the staggered magnetization curve, the core of the paper is a calculation at the tree level, of the Green functions of the model. We obtain precise results for the elementary excitation spectrum and in particular for the spin gaps in the transverse and longitudinal channels. It is shown that, while the spectral weight in the transverse channel is exhausted by a single magnon pole, in the longitudinal one, besides a magnon pole a two-magnon continuum appears as well whose weight is a steadily increasing function of the applied field, while the weight of the magnon decreases correspondingly. The balance between the two is governed by a sum rule that is derived and discussed. A detailed comparison with the present experimental and numerical state of the art as well as with previous analytical approaches is also made.

arXiv:cond-mat/0007188•Physical review. B, Condensed matter•Dec 1, 2000•19 citations

Low-energy properties of anisotropic two-dimensional spin- 12 Heisenberg models in staggered magnetic fields

Bin Xi, Shijie Hu, Jize Zhao +3 more

We present a systematic study of the anisotropic spin-1/2 Heisenberg model in staggered magnetic fields in two dimensions. To mimic real materials, we consider a system of coupled, antiferromagnetic chains, whose interchain interaction can be either ferro- or antiferromagnetic. When the staggered field is commensurate with the magnetic interactions, an energy gap opens immediately and follows a power law as a function of the applied field, similar to the situation in one dimension. When the field competes with the interactions, a quantum phase transition (QPT) occurs from a gapless, magnetically ordered phase at low fields to a gapped, disordered regime. We use a continuous-time Monte Carlo method to compute the staggered moment of the ordered phases and the spin gap of the disordered phases. We deduce the phase diagrams as functions of the anisotropy ratio and the applied field, and calculate the scaling behavior of the models in both quantities. We show that in the competitive case, the staggered field acts to maintain a regime of quasi-1D behavior around the QPT, and we discuss as a consequence the nature of the crossover from one-dimensional (1D) to 2D physics.

arXiv:1106.4605•Physical Review B•Oct 10, 2011•11 citations
We study the properties of one-dimensional gapped Heisenberg antiferromagnets in the presence of a strong staggered magnetic field. For these systems we predict a universal form for the staggered magnetization curve. This function, as well as the effect the staggered field has on the energy gaps in longitudinal and transversal excitation spectra, is determined from the universal form of the effective potential in O(3)O(3)O(3)-symmetric (1+1)(1+1)(1+1)-dimensional field theory. Our theoretical findings are in excellent agreement with recent neutron scattering data on R2BaNiO5{R}_{2}{\mathrm{BaNiO}}_{5}R2​BaNiO5​ ( R=R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}R= magnetic rare earth) linear-chain mixed spin antiferromagnets.
Using the density-matrix-renormalization-group technique, we calculate numerically the low-energy excitation spectrum and magnetization curve of the spin-1 antiferromagnetic chain in a staggered magnetic field, which is expected to describe the physics of the ${R}_{2}{\mathrm{BaNiO}}_{5} (R\ensuremath{\ne}Y)$ family below the N\'eel temperature of the magnetic rare-earth (R) sublattice. These results are valid in the entire range of the staggered field, and agree with those given by the nonlinear $\ensuremath{\sigma}$ model study for small fields, but differ from the latter for large fields. They are consistent with the available experimental data. The correlation functions for this model are also calculated. The transverse correlations display the anticipated exponential decay with shorter correlation length, while the longitudinal correlations show explicitly the induced staggered magnetization.
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.
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.
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.
We present in this paper a nonlinear \ensuremath{\sigma}-model analysis of a spin-1 antiferromagnetic Heisenberg chain in an external commensurate staggered magnetic field. After rediscussing briefly and extending previous results for the staggered magnetization curve, the core of the paper is a calculation at the tree level, of the Green functions of the model. We obtain precise results for the elementary excitation spectrum and in particular for the spin gaps in the transverse and longitudinal channels. It is shown that, while the spectral weight in the transverse channel is exhausted by a single magnon pole, in the longitudinal one, besides a magnon pole a two-magnon continuum appears as well whose weight is a steadily increasing function of the applied field, while the weight of the magnon decreases correspondingly. The balance between the two is governed by a sum rule that is derived and discussed. A detailed comparison with the present experimental and numerical state of the art as well as with previous analytical approaches is also made.
We present a systematic study of the anisotropic spin-1/2 Heisenberg model in staggered magnetic fields in two dimensions. To mimic real materials, we consider a system of coupled, antiferromagnetic chains, whose interchain interaction can be either ferro- or antiferromagnetic. When the staggered field is commensurate with the magnetic interactions, an energy gap opens immediately and follows a power law as a function of the applied field, similar to the situation in one dimension. When the field competes with the interactions, a quantum phase transition (QPT) occurs from a gapless, magnetically ordered phase at low fields to a gapped, disordered regime. We use a continuous-time Monte Carlo method to compute the staggered moment of the ordered phases and the spin gap of the disordered phases. We deduce the phase diagrams as functions of the anisotropy ratio and the applied field, and calculate the scaling behavior of the models in both quantities. We show that in the competitive case, the staggered field acts to maintain a regime of quasi-1D behavior around the QPT, and we discuss as a consequence the nature of the crossover from one-dimensional (1D) to 2D physics.