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

Physical review. B./Physical review. B

Observation of Bethe strings in the quantum spin chain antiferromagnet BaCo 2 V 2 O 8

K. Puzniak, A. T. M. N. Islam, Xiaotong Chen, Jiahao Yang, P. Steffens, Martin Boehm, Jianda Wu, B. Lake

Published Apr 16, 2026• 0 citations
Publisher

Abstract

Despite being predicted almost a century ago as the excitations of the spin-1/2 antiferromagnetic chain, Bethe strings were overshadowed by the more dominant multi-spinon-pair excitations and were only observed recently. Here we confirm their existence in the quasi-one-dimensional quantum antiferromagnet BaCo 2 V 2 O 8 using a magnetic field to separate them from the spinons. We find excellent quantitative agreement over an extended field range between these experimental results and our theoretical predictions based on the algebraic Bethe ansatz formalism. This work proves the existence of Bethe strings (multimagnon bound states) up to length-3 in BaCo 2 V 2 O 8 .

DOI
10.1103/5n46-c5k4

Related papers

Quantum Critical Dynamics of a Heisenberg-Ising Chain in a Longitudinal Field: Many-Body Strings versus Fractional Excitations

Zhe Wang, M. Schmidt, Alois Loidl +11 more

We report a high-resolution terahertz spectroscopic study of quantum spin dynamics in the antiferromagnetic Heisenberg-Ising spin-chain compound BaCo_{2}V_{2}O_{8} as a function of temperature and longitudinal magnetic field. Confined spinon excitations are observed in an antiferromagnetic phase below T_{N}≃5.5 K. In a field-induced gapless phase above B_{c}=3.8 T, we identify many-body string excitations as well as low-energy fractional psinon or antipsinon excitations by comparing to Bethe ansatz calculations. In the vicinity of B_{c}, the high-energy string excitations are found to have a dominant contribution to the spin dynamics as compared with the fractional excitations.

arXiv:1903.05492•Physical Review Letters•Aug 6, 2019•48 citations

Confinement of many-body Bethe strings

Jiahao Yang, Tao Xie, Stanislav E. Nikitin +2 more

Based on the Bethe ansatz approach and inelastic neutron scattering experiments, we reveal the evolution of confinement of many-body Bethe strings in ordered regions of the quasi-one-dimensional antiferromagnet ${\mathrm{YbAlO}}_{3}$. In the antiferromagnetic phase, the spin dynamics is dominated by confined length-1 Bethe strings, whose dominancy in the high-energy branch of the excitation spectrum yields to confined length-2 Bethe strings when the material is tuned to the spin-density-wave phase. In the thermal-induced disordered region, the confinement effect disappears, and the system restores the conventional quantum integrable physics of the one-dimensional Heisenberg model. Our results establish a unified picture based on a Bethe string for the spin dynamics in different magnetic phases of ${\mathrm{YbAlO}}_{3}$, and thus provide profound insight into many-body quantum magnetism.

arXiv:2212.03442•Physical review. B./Physical review. B•Jul 18, 2023•5 citations

Line-shape predictions via Bethe ansatz for the one-dimensional spin- 12 Heisenberg antiferromagnet in a magnetic field

Michael Karbach, Gerhard H. Muller

The spin fluctuations parallel to the external magnetic field in the ground state of the one-dimensional (1D) $s=\frac{1}{2}$ Heisenberg antiferromagnet are dominated by a two-parameter set of collective excitations. In a cyclic chain of N sites and magnetization $0<{M}_{z}<N/2,$ the ground state, which contains ${2M}_{z}$ spinons, is reconfigured as the physical vacuum for a different species of quasiparticles, identifiable in the framework of the coordinate Bethe ansatz by characteristic configurations of Bethe quantum numbers. The dynamically dominant excitations are found to be scattering states of two such quasiparticles. For $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty},$ these collective excitations form a continuum in $(q,\ensuremath{\omega})$ space with an incommensurate soft mode. Their matrix elements in the dynamic spin structure factor ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ are calculated directly from the Bethe wave functions for finite N. The resulting line- shape predictions for $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ complement the exact results previously derived via algebraic analysis for the exact two-spinon part of ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ in the zero-field limit. They are relevant for neutron-scattering experiments on quasi-1D antiferromagnetic compounds in a strong magnetic field.

arXiv:cond-mat/0005174•Physical review. B, Condensed matter•Dec 1, 2000•51 citations

Quasiparticles of string solutions in the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field

Masanori Kohno

Spectral properties of the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field are investigated by using exact Bethe-ansatz solutions. We argue that not only quasiparticles called psinon and antipsinon but also a quasiparticle representing a 2-string in the Bethe ansatz plays an important role for dynamical properties in a magnetic field. Combined with psinon and antipsinon, the quasiparticle for a 2-string forms a continuum in the high-energy regime for transverse dynamical structure factor S +− ( κ,ω ). In the zero-field limit, the continuum is located on the mode of the lowest excited states in zero field called the des Cloizeaux-Pearson mode. In a magnetic field, the continuum separates from other low-energy continua, and reduces to the mode of bound states of overturned spins from the fully polarized state near the saturation field. We confirm the relevance through comparisons with available experimental results on the quasi-one-dimensional antiferromagnet CuCl 2 ·2N(C 5 D 5 ).

arXiv:1201.0844•Journal of Physics Conference Series•Jan 1, 2010•3 citations

Exceptional E$_8$ symmetry in spin dynamics of quasi-one-dimensional antiferromagnet BaCo$_2$V$_2$O$_8$

Haiyuan Zou, Yuliang Cui, X. Wang +7 more

Exotic excitations can emerge in the vicinity of a quantum phase transition. When the quantum critical point of the one-dimensional (1D) transverse field Ising model is perturbed by a longitudinal magnetic field, it was predicted that its massive excitations are precisely described by the exceptional E$_8$ Lie algebra. Here we show an unambiguous experimental realization of the massive E$_8$ phase in the quasi-1D antiferromagnetic material BaCo$_2$V$_2$O$_8$, via nuclear magnetic resonance and inelastic neutron scattering measurements, and detailed theoretical analysis. The large separation between the masked 1D and 3D quantum critical points of the system allows us to identify, for the first time, the full 8 single-particle E$_8$ excitations as well as various multi-particle states in the spin excitation spectrum. Our results open new experimental route for exploring the dynamics of quantum integrable systems and physics beyond integrability, and thus bridge key physics in condensed matter and statistical field theory.

•May 27, 2020•1 citation

Truncated string state space approach and its application to the nonintegrable spin- 1 2 Heisenberg chain

Jiahao Yang, Jianda Wu

By circumventing the difficulty of obtaining exact string state solutions to Bethe ansatz equations, we devise a truncated string state space approach for investigating spin dynamics in a nonintegrable spin-$\frac{1}{2}$ Heisenberg chain subjected to a staggered field at various magnetizations. The obtained dynamical spectra reveal a series of elastic peaks at integer multiples of the ordering wave vector $Q$, indicating the presence of multi-$Q$ Bethe string states within the ground state. The spectrum exhibits a separation between different string continua as the strength of the staggered field increases at low magnetization, reflecting the confinement of the Bethe strings. This approach provides a unified string-state-based framework for understanding spin dynamics in low-dimensional nonintegrable Heisenberg models, which has a successful application to observations across various phases of the quasi-one-dimensional antiferromagnet ${\mathrm{YbAlO}}_{3}$.

arXiv:2401.02018•Physical review. B./Physical review. B•Jun 14, 2024•3 citations
Despite being predicted almost a century ago as the excitations of the spin-1/2 antiferromagnetic chain, Bethe strings were overshadowed by the more dominant multi-spinon-pair excitations and were only observed recently. Here we confirm their existence in the quasi-one-dimensional quantum antiferromagnet BaCo 2 V 2 O 8 using a magnetic field to separate them from the spinons. We find excellent quantitative agreement over an extended field range between these experimental results and our theoretical predictions based on the algebraic Bethe ansatz formalism. This work proves the existence of Bethe strings (multimagnon bound states) up to length-3 in BaCo 2 V 2 O 8 .
We report a high-resolution terahertz spectroscopic study of quantum spin dynamics in the antiferromagnetic Heisenberg-Ising spin-chain compound BaCo_{2}V_{2}O_{8} as a function of temperature and longitudinal magnetic field. Confined spinon excitations are observed in an antiferromagnetic phase below T_{N}≃5.5 K. In a field-induced gapless phase above B_{c}=3.8 T, we identify many-body string excitations as well as low-energy fractional psinon or antipsinon excitations by comparing to Bethe ansatz calculations. In the vicinity of B_{c}, the high-energy string excitations are found to have a dominant contribution to the spin dynamics as compared with the fractional excitations.
Based on the Bethe ansatz approach and inelastic neutron scattering experiments, we reveal the evolution of confinement of many-body Bethe strings in ordered regions of the quasi-one-dimensional antiferromagnet YbAlO3{\mathrm{YbAlO}}_{3}YbAlO3​. In the antiferromagnetic phase, the spin dynamics is dominated by confined length-1 Bethe strings, whose dominancy in the high-energy branch of the excitation spectrum yields to confined length-2 Bethe strings when the material is tuned to the spin-density-wave phase. In the thermal-induced disordered region, the confinement effect disappears, and the system restores the conventional quantum integrable physics of the one-dimensional Heisenberg model. Our results establish a unified picture based on a Bethe string for the spin dynamics in different magnetic phases of YbAlO3{\mathrm{YbAlO}}_{3}YbAlO3​, and thus provide profound insight into many-body quantum magnetism.
The spin fluctuations parallel to the external magnetic field in the ground state of the one-dimensional (1D) s=12s=\frac{1}{2}s=21​ Heisenberg antiferromagnet are dominated by a two-parameter set of collective excitations. In a cyclic chain of N sites and magnetization 0<Mz<N/2,0<{M}_{z}<N/2,0<Mz​<N/2, the ground state, which contains 2Mz{2M}_{z}2Mz​ spinons, is reconfigured as the physical vacuum for a different species of quasiparticles, identifiable in the framework of the coordinate Bethe ansatz by characteristic configurations of Bethe quantum numbers. The dynamically dominant excitations are found to be scattering states of two such quasiparticles. For $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty},$ these collective excitations form a continuum in $(q,\ensuremath{\omega})$ space with an incommensurate soft mode. Their matrix elements in the dynamic spin structure factor ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ are calculated directly from the Bethe wave functions for finite N. The resulting line- shape predictions for $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ complement the exact results previously derived via algebraic analysis for the exact two-spinon part of ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ in the zero-field limit. They are relevant for neutron-scattering experiments on quasi-1D antiferromagnetic compounds in a strong magnetic field.
Spectral properties of the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field are investigated by using exact Bethe-ansatz solutions. We argue that not only quasiparticles called psinon and antipsinon but also a quasiparticle representing a 2-string in the Bethe ansatz plays an important role for dynamical properties in a magnetic field. Combined with psinon and antipsinon, the quasiparticle for a 2-string forms a continuum in the high-energy regime for transverse dynamical structure factor S +− ( κ,ω ). In the zero-field limit, the continuum is located on the mode of the lowest excited states in zero field called the des Cloizeaux-Pearson mode. In a magnetic field, the continuum separates from other low-energy continua, and reduces to the mode of bound states of overturned spins from the fully polarized state near the saturation field. We confirm the relevance through comparisons with available experimental results on the quasi-one-dimensional antiferromagnet CuCl 2 ·2N(C 5 D 5 ).
Exceptional E8_88​ symmetry in spin dynamics of quasi-one-dimensional antiferromagnet BaCo2_22​V2_22​O8_88​
Exotic excitations can emerge in the vicinity of a quantum phase transition. When the quantum critical point of the one-dimensional (1D) transverse field Ising model is perturbed by a longitudinal magnetic field, it was predicted that its massive excitations are precisely described by the exceptional E8_88​ Lie algebra. Here we show an unambiguous experimental realization of the massive E8_88​ phase in the quasi-1D antiferromagnetic material BaCo2_22​V2_22​O8_88​, via nuclear magnetic resonance and inelastic neutron scattering measurements, and detailed theoretical analysis. The large separation between the masked 1D and 3D quantum critical points of the system allows us to identify, for the first time, the full 8 single-particle E8_88​ excitations as well as various multi-particle states in the spin excitation spectrum. Our results open new experimental route for exploring the dynamics of quantum integrable systems and physics beyond integrability, and thus bridge key physics in condensed matter and statistical field theory.
By circumventing the difficulty of obtaining exact string state solutions to Bethe ansatz equations, we devise a truncated string state space approach for investigating spin dynamics in a nonintegrable spin-12\frac{1}{2}21​ Heisenberg chain subjected to a staggered field at various magnetizations. The obtained dynamical spectra reveal a series of elastic peaks at integer multiples of the ordering wave vector QQQ, indicating the presence of multi-QQQ Bethe string states within the ground state. The spectrum exhibits a separation between different string continua as the strength of the staggered field increases at low magnetization, reflecting the confinement of the Bethe strings. This approach provides a unified string-state-based framework for understanding spin dynamics in low-dimensional nonintegrable Heisenberg models, which has a successful application to observations across various phases of the quasi-one-dimensional antiferromagnet YbAlO3{\mathrm{YbAlO}}_{3}YbAlO3​.