arXiv:2403.10785 · Physical review. B./Physical review. B

Emergent D 8 ( 1 ) spectrum and topological soliton excitation in CoNb 2 O 6

Ning Xi, Xiao Wang, Yunjing Gao, Yunfeng Jiang, Rong Yu, Jianda Wu

Published Nov 8, 2025• 1 citation

Abstract

Quantum integrability emerging near a quantum critical point (QCP) is manifested by an exotic excitation spectrum that is organized by the associated algebraic structure. A well-known example is the emergent ${E}_{8}$ integrability near the QCP of a transverse field Ising chain (TFIC), which was long predicted theoretically and initially proposed to be realized in the quasi-one-dimensional (q1D) quantum magnet ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$. However, later measurements on the spin excitation spectrum of this material revealed a series of satellite peaks in low energies that go beyond the description of the ${E}_{8}$ Lie algebra. Motivated by this experimental progress, we hereby revisit the spin excitations of ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ by combining numerical calculation and analytical analysis. We show that, as effects of strong interchain fluctuations, the spectrum of the system near the 1D QCP is characterized by an emergent ${D}_{8}^{(1)}$ Lie algebra instead of the ${E}_{8}$ one. We further show that the ${D}_{8}^{(1)}$ spectrum can be realized in a broad class of interacting quantum systems. Our results advance the exploration and manipulation of integrability in quantum critical systems.

DOI: 10.1103/f32m-kkzm

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arXiv:2403.10785 · Physical review. B./Physical review. B

Emergent D 8 ( 1 ) spectrum and topological soliton excitation in CoNb 2 O 6

Ning Xi, Xiao Wang, Yunjing Gao, Yunfeng Jiang, Rong Yu, Jianda Wu

Published Nov 8, 2025• 1 citation

arXiv HTML PDF

Abstract

{E}_{8}

integrability near the QCP of a transverse field Ising chain (TFIC), which was long predicted theoretically and initially proposed to be realized in the quasi-one-dimensional (q1D) quantum magnet

{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}

. However, later measurements on the spin excitation spectrum of this material revealed a series of satellite peaks in low energies that go beyond the description of the

{E}_{8}

Lie algebra. Motivated by this experimental progress, we hereby revisit the spin excitations of

{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}

by combining numerical calculation and analytical analysis. We show that, as effects of strong interchain fluctuations, the spectrum of the system near the 1D QCP is characterized by an emergent

{D}_{8}^{(1)}

Lie algebra instead of the

{E}_{8}

one. We further show that the

{D}_{8}^{(1)}

spectrum can be realized in a broad class of interacting quantum systems. Our results advance the exploration and manipulation of integrability in quantum critical systems.

DOI: 10.1103/f32m-kkzm

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

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cond-mat.str-elCross-listedarXiv:2607.23547Jul 28, 20260 citations

{E}_{8}

integrability near the QCP of a transverse field Ising chain (TFIC), which was long predicted theoretically and initially proposed to be realized in the quasi-one-dimensional (q1D) quantum magnet

{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}

. However, later measurements on the spin excitation spectrum of this material revealed a series of satellite peaks in low energies that go beyond the description of the

{E}_{8}

Lie algebra. Motivated by this experimental progress, we hereby revisit the spin excitations of

{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}

by combining numerical calculation and analytical analysis. We show that, as effects of strong interchain fluctuations, the spectrum of the system near the 1D QCP is characterized by an emergent

{D}_{8}^{(1)}

Lie algebra instead of the

{E}_{8}

one. We further show that the

{D}_{8}^{(1)}

spectrum can be realized in a broad class of interacting quantum systems. Our results advance the exploration and manipulation of integrability in quantum critical systems.

Exceptional E

_8

symmetry in spin dynamics of quasi-one-dimensional antiferromagnet BaCo

_2

_2

_8

_8

Lie algebra. Here we show an unambiguous experimental realization of the massive E

_8

phase in the quasi-1D antiferromagnetic material BaCo

_2

_2

_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.

{E}_{8}

Lie algebra. Here we report on high-resolution terahertz spectroscopy of quantum spin dynamics in the ferromagnetic Ising-chain material

{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}

. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six

{E}_{8}

particles,

{\mathrm{m}}_{1}

{\mathrm{m}}_{6}

, and the two-particle

({\mathrm{m}}_{1}+{\mathrm{m}}_{2})

continuum in an applied transverse magnetic field of

{B}_{c}^{\text{1D}}=4.75 \mathrm{T}

, before the three-dimensional magnetic order is suppressed above ${B}_{c}^{\text{3D}}\ensuremath{\approx}5.3 \mathrm{T}$. The observation of the higher-energy particles

({\mathrm{m}}_{3} \mathrm{to} {\mathrm{m}}_{6})

above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.

{E}_{8}

Lie algebra, but rarely explored experimentally. Here we use high-resolution terahertz spectroscopy to resolve quantum spin dynamics of the quasi-one-dimensional Ising antiferromagnet

\mathrm{BaC}{\mathrm{o}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}

in an applied transverse field. By comparing to an analytical calculation of the dynamical spin correlations, we identify

{E}_{8}

particles as well as their two-particle excitations.

E_8

Lie algebra. In this work, we report on experimental observation of a characteristic massive spectrum close to transverse field-induced dimensional reduction in a quasi-two-dimensional quantum magnet Cu

_2

(OH)

_3

Br, providing evidence for an emergent

E_8

symmetry and the corresponding excitations of bound states in the sublattice of its ferromagnetic chains. These results demonstrate the power of integrable field theory in describing emergent many-body quantum critical phenomena in condensed matter systems.