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

Abstract

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 CoNb 2 O 6. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six E 8 particles, m 1 to m 6 , and the two-particle (m 1 + m 2) continuum in an applied transverse magnetic field of B 1D c = 4.75 T, before the three-dimensional magnetic order is suppressed above B 3D c ≈ 5.3 T. The observation of the higher-energy particles (m 3 to m 6) above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.

Cascade of singularities in the spin dynamics of a perturbed quantum critical Ising chain

“…In this article, we provided a systematic theoretical analysis that greatly expands the theoretical treatment of Refs. [21,22,31] and which will also be helpful in guiding a realization of the E 8 model in other possible materials, such as CoNb 2 O 6 [31]. In BCVO, the QCP of TFIC universality is hidden in the 3D ordered phase with an inter-chain interaction serving as the longitudinal perturbation [22].…”

“…In BCVO, the QCP of TFIC universality is hidden in the 3D ordered phase with an inter-chain interaction serving as the longitudinal perturbation [22]. The obtained theoretical DSF can be directly measured by terahertz spectroscopy measurements [21,31] as well as inelastic neutron scattering experiments [22]. The experimentally measured differential cross section is related to the DSF by [32]…”

Quantum phase transitions in a quasi-one-dimensional Ising quantum magnet in transverse fields

“…The ratios of the masses of the eight E 8 particles are related to the roots of the E 8 algebra and can be determined analytically [18,19]. The first two meson particles of the E 8 excitations spectrum were indeed observed in the quasi-1D Ising ferromagnet CoNb 2 O 6 [4,20]. Very recently, inelastic neutron scattering (INS) and the terahertz spectroscopy measurements have revealed a series of sharp modes in BaCo 2 V 2 O 8 under applied field of 4.7 T along the tetragonal b direction [16,17].…”

Quantum Critical Magnetic Excitations in Spin-1/2 and Spin-1 Chain Systems

“…For instance, by mapping to a spinless fermion system, the transverse-field Ising chain (TFIC) model can be exactly solved [5,6]. The closest realization of this model has long been thought to be CoNb 2 O 6 under a transverse field [7][8][9][10][11][12][13][14][15][16][17].…”

“…Central to these studies is the detection of the magnetic excitations across the QCP [10][11][12][13][14][15][16]23]. In low-energy probes like nuclear magnetic resonance, the quasielastic mode associated with domain-wall quasiparticles (kinks) was found to disappear above the 1D QCP [11].…”