Observation of E8 particles in an Ising chain antiferromagnet

Abstract

Near the transverse-field induced quantum critical point of the Ising chain, an exotic dynamic spectrum consisting of exactly eight particles was predicted, which is uniquely described by an emergent quantum integrable field theory with the symmetry of the E8 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 BaCo2V2O8 in an applied transverse field. By comparing to an analytical calculation of the dynamical spin correlations, we identify E8 particles as well as their two-particle excitations.

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

“…Motivated by these theoretical results, we experimentally revisited the spin dynamic spectrum in CoNb 2 O 6 by performing high-resolution terahertz spectroscopy in an applied transverse magnetic field. We identify not only the two lowest E 8 particles but also the higher-energy ones up to m 6 , as well as the peaklike maximum of the two-particle continuum (m 1 + m 2 ), confirming the theoretical predictions of the 1D quantum many-body system [17,35,36].…”

“…Moreover, the two-particle continuum (m 1 + m 2 ) was found to be characterized by a peaklike maximum at the onset energy, and thus potentially resolvable on top of the (m 1 + m 1 ) continuum. Very recently the findings of the numerical simulations were supported by rigorous quantum field theory analysis of the dynamic spectra of the two-particle continua [35,36], which revealed that the spectral weight of the (m 1 + m 1 ) continuum decreases considerably with increasing energy, becoming relatively weak particularly at the energies where the higher-energy particles are predicted to appear. Moreover, it showed that the two-particle continua, such as (m 1 + m 1 ) and (m 1 + m 2 ), are not featureless but characterized by a peaklike maximum at the onset energies which is followed by an extended tail towards higher energies [35,36].…”

“…Very recently the findings of the numerical simulations were supported by rigorous quantum field theory analysis of the dynamic spectra of the two-particle continua [35,36], which revealed that the spectral weight of the (m 1 + m 1 ) continuum decreases considerably with increasing energy, becoming relatively weak particularly at the energies where the higher-energy particles are predicted to appear. Moreover, it showed that the two-particle continua, such as (m 1 + m 1 ) and (m 1 + m 2 ), are not featureless but characterized by a peaklike maximum at the onset energies which is followed by an extended tail towards higher energies [35,36]. These theoretical results clearly showed the exotic dynamic features of this quantum many-body system, in contrast to the conventional understanding drawing from a single-particle picture.…”

“…Using a Sciencetech SPS200 Martin-Puplett-type spectrometer, field-dependent terahertz transmission measurements were carried out at 4 K (above T C ) and 0.25 K (below T C ) with a liquid-helium bath cryostat and a 3 He - 4 He dilution fridge, respectively, using bolometers operating at 0.3 and 0.4 K as detectors. For the 4 K experiment, a rotatable polarizer was placed in front of the sample for tuning polarization of the terahertz waves [35,44]. For the 0.25 K measurements the sample cell was attached to the cold finger of the dilution fridge (Oxford Instruments), which was equipped with a superconducting solenoid for applying a magnetic field.…”

“…The absence of the higher-energy E 8 particles m 3 to m 8 in the inelastic neutron scattering spectra was assumed to be a consequence of an overwhelming (m 1 + m 1 ) continuum [15], since it is energetically more favorable to excite two m 1 particles, as m 3 2m 1 < m 4 , m 5 , m 8 . This notion may be more natural for noninteracting particles, but it is not necessarily applicable to the concerned quantum many-body system [17,35,36]. Using the time-evolving block decimation, a numerical study [17] showed that the higher-energy E 8 particles up to m 5 should stand out as sharp peaks in the dynamic spectrum, whereas the (m 1 + m 1 ) continuum contributes a relatively small background.…”