Physics Today

A complex symmetry arises at a spin chain’s quantum critical point

Barbara Goss Levi

Published Feb 26, 2010• 8 citations

Abstract

The relation between the E8 Lie group and the mass excitations in the Ising model was predicted more than 20 years ago, but seeing it is an experimental coup.

DOI: 10.1063/1.3366227

Related papers

How a complex Zeeman field drives quantum phase transitions in the Ising model: From the perspective of geometric phase and symmetry

D.L. Wen, M.L. Li

OptikSep 27, 20210 citations

Meson spectroscopy of exotic symmetries of Ising criticality in Rydberg atom arrays

Joseph Vovrosh, Julius de Hond, Sergi Julià-Farré +2 more

arXiv:2506.21299Jun 26, 20250 citations

Spin dynamics of a perturbed quantum critical Ising chain

Xiao Wang, Haiyuan Zou, Kristóf Hódsági +3 more

Bulletin of the American Physical SocietyMar 15, 20210 citations

Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E 8 Symmetry

R. Coldea, D. M. Tennant, Elisa M. Wheeler +6 more

arXiv:1103.3694ScienceJan 7, 2010731 citations

Experimental observation of quantum many-body excitations of E8 symmetry in the Ising chain ferromagnet CoNb2O6

Kirill Amelin, Johannes Engelmayer, J. Viirok +4 more

arXiv:2006.12956Physical review. B./Physical review. BSep 24, 202042 citations

Excitations of critical quantum spin chains from non-equilibrium classical dynamics

Stphane Vinet, Gabriel Longpré, William Witczak‐Krempa

Bulletin of the American Physical SocietyMar 16, 20210 citations

Physics Today

A complex symmetry arises at a spin chain’s quantum critical point

Barbara Goss Levi

Published Feb 26, 2010• 8 citations

Publisher

Abstract

The relation between the E8 Lie group and the mass excitations in the Ising model was predicted more than 20 years ago, but seeing it is an experimental coup.

DOI: 10.1063/1.3366227

Related papers

How a complex Zeeman field drives quantum phase transitions in the Ising model: From the perspective of geometric phase and symmetry

D.L. Wen, M.L. Li

OptikSep 27, 20210 citations

Meson spectroscopy of exotic symmetries of Ising criticality in Rydberg atom arrays

Joseph Vovrosh, Julius de Hond, Sergi Julià-Farré +2 more

The Ising model serves as a canonical platform for exploring emergent symmetry in quantum critical systems. The critical point of the 1D Ising chain is described by a conformal Ising field theory, which remains integrable in the presence of a magnetic perturbation, leading to massive particles associated with the exceptional Lie algebra $E_8$ . Weakly coupling two Ising chains into a ladder breaks this integrability and is predicted to confine the elementary excitations of each chain into a richer spectrum of bound states organized by a $\mathcal{D}^{(1)}_8$ symmetry. Experimental signatures of $E_8$ excitations have arguably been observed in scattering studies of the spin chain material CoNb $_2$ O $_6$ , but direct evidence of confinement driven by inter-chain coupling has remained elusive. Here, we probe these emergent symmetries in a Rydberg atom quantum processing unit, leveraging its tunable geometry to realize both chain and ladder configurations. We identify mass spectra consistent with $E_8$ at the single-chain critical point and, in the weakly coupled ladder, report the first signatures of confinement of Ising excitations into the bound-state spectrum predicted by $\mathcal{D}^{(1)}_8$ symmetry. Our results demonstrate the power of Rydberg platforms for investigating symmetry emergence in quantum many-body systems and provide a direct window into the interplay of confinement, geometry, and criticality.The Ising model serves as a canonical platform for exploring emergent symmetry in quantum critical systems. The critical point of the 1D Ising chain is described by a conformal Ising field theory, which remains integrable in the presence of a magnetic perturbation, leading to massive particles associated with the exceptional Lie algebra $E_8$. Weakly coupling two Ising chains into a ladder breaks this integrability and is predicted to confine the elementary excitations of each chain into a richer spectrum of bound states organized by a $\mathcal{D}^{(1)}_8$ symmetry. Experimental signatures of $E_8$ excitations have arguably been observed in scattering studies of the spin chain material CoNb$_2$O$_6$, but direct evidence of confinement driven by inter-chain coupling has remained elusive. Here, we probe these emergent symmetries in a Rydberg atom quantum processing unit, leveraging its tunable geometry to realize both chain and ladder configurations. We identify mass spectra consistent with $E_8$ at the single-chain critical point and, in the weakly coupled ladder, report the first signatures of confinement of Ising excitations into the bound-state spectrum predicted by $\mathcal{D}^{(1)}_8$ symmetry. Our results demonstrate the power of Rydberg platforms for investigating symmetry emergence in quantum many-body systems and provide a direct window into the interplay of confinement, geometry, and criticality.

arXiv:2506.21299Jun 26, 20250 citations

Spin dynamics of a perturbed quantum critical Ising chain

Xiao Wang, Haiyuan Zou, Kristóf Hódsági +3 more

Bulletin of the American Physical SocietyMar 15, 20210 citations

Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E 8 Symmetry

R. Coldea, D. M. Tennant, Elisa M. Wheeler +6 more

Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8 Lie group with a spectrum of eight particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by using strong transverse magnetic fields to tune the quasi-one-dimensional Ising ferromagnet CoNb2O6 (cobalt niobate) through its critical point. Spin excitations are observed to change character from pairs of kinks in the ordered phase to spin-flips in the paramagnetic phase. Just below the critical field, the spin dynamics shows a fine structure with two sharp modes at low energies, in a ratio that approaches the golden mean predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviors.Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8 Lie group with a spectrum of eight particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by using strong transverse magnetic fields to tune the quasi-one-dimensional Ising ferromagnet CoNb2O6 (cobalt niobate) through its critical point. Spin excitations are observed to change character from pairs of kinks in the ordered phase to spin-flips in the paramagnetic phase. Just below the critical field, the spin dynamics shows a fine structure with two sharp modes at low energies, in a ratio that approaches the golden mean predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviors.

arXiv:1103.3694ScienceJan 7, 2010731 citations

Experimental observation of quantum many-body excitations of E8 symmetry in the Ising chain ferromagnet CoNb2O6

Kirill Amelin, Johannes Engelmayer, J. Viirok +4 more

Close to the quantum critical point of the transverse-field Ising spin-chain model, an exotic dynamic spectrum was predicted to emerge upon a perturbative longitudinal field. The dynamic spectrum consists of eight particles and is governed by the symmetry of the ${E}_{8}$ 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, ${\mathrm{m}}_{1}$ to ${\mathrm{m}}_{6}$ , 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.Close to the quantum critical point of the transverse-field Ising spin-chain model, an exotic dynamic spectrum was predicted to emerge upon a perturbative longitudinal field. The dynamic spectrum consists of eight particles and is governed by the symmetry of the ${E}_{8}$ 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, ${\mathrm{m}}_{1}$ to ${\mathrm{m}}_{6}$, 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.

arXiv:2006.12956Physical review. B./Physical review. BSep 24, 202042 citations

Excitations of critical quantum spin chains from non-equilibrium classical dynamics

Stphane Vinet, Gabriel Longpré, William Witczak‐Krempa

Bulletin of the American Physical SocietyMar 16, 20210 citations

E_8

. Weakly coupling two Ising chains into a ladder breaks this integrability and is predicted to confine the elementary excitations of each chain into a richer spectrum of bound states organized by a

\mathcal{D}^{(1)}_8

symmetry. Experimental signatures of

E_8

excitations have arguably been observed in scattering studies of the spin chain material CoNb

_2

_6

, but direct evidence of confinement driven by inter-chain coupling has remained elusive. Here, we probe these emergent symmetries in a Rydberg atom quantum processing unit, leveraging its tunable geometry to realize both chain and ladder configurations. We identify mass spectra consistent with

E_8

at the single-chain critical point and, in the weakly coupled ladder, report the first signatures of confinement of Ising excitations into the bound-state spectrum predicted by

\mathcal{D}^{(1)}_8

symmetry. Our results demonstrate the power of Rydberg platforms for investigating symmetry emergence in quantum many-body systems and provide a direct window into the interplay of confinement, geometry, and criticality.

{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.