From the transverse-field Ising chain to the quantum E8 integrable model: Theoretical progress and experimental realization*

Exotic thermodynamics and excitations can emerge in the vicinity of a quantum phase transition. In the talk, I will first detailedly discuss the very unique quantum criticality for the Grüneisen ratio in the transverse field Ising chain (TFIC) [1], which then serves as a smoking gun to identify the underlying TFIC universality observed in quasi-one-dimensional (1D) antiferromagnetic material BaCo₂V₂O₈ with transverse field applied along [110] direction [2]. From systematic quantum critical analysis for the effective model of the material [3], we confirm SrCo₂V₂O₈ with field applied along [100] direction can also accommodate the TFIC universality with much weaker magnetic field [4]. Furthermore, when the quantum critical point (QCP) of the TFIC is perturbed by a longitudinal magnetic field, it was predicted that its massive excitations are precisely described by the exceptional E₈ Lie algebra. Here we show an unambiguous experimental realization of the massive E₈ phase in the material BaCo₂V₂O₈, via NMR and inelastic neutron scattering measurements, and detailed theoretical analysis [5, 6, 7]. The large separation between the masked 1D and 3D QCPs of the system allows us to identify, for the first time, the full 8 single-particle E₈ excitations and various multi-E₈-particle states in the spin excitation spectrum. Our results open new experimental and theoretical 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.

[1] Phys. Rev B 97, 245127 (2018).

[2] Phys. Rev. Lett. 120, 207205 (2018).

[3] J. Phys. Condens. Matter. 32, 045602 (2020).

[4] Phys. Rev. Lett. 123, 067203 (2019).

[5] Phys. Rev. B 101, 220411(R) (2020).

[6] Phys. Rev. B 103, 235117 (2021).

[7] Phys. Rev. Lett. 127, 077201 (2021).