Wang, X.; Puzniak, K.; Schmalzl, K.; Balz, C.; Matsuda, M.; Okutani, A.; Hagiwara, M.; Ma, J.; Wu, J.; Lake, B.: Spin dynamics of the E8 particles. Science Bulletin 69 (2024), p. 2974-2977
10.1016/j.scib.2024.07.040
Open Access Version
Abstract:
Unlike the classical phase transition driven by thermal fluctuations, the quantum phase transition arises at zero temperature when the system is tuned by a non-thermal parameter [1]. For a continuous quantum phase transition, novel physics with higher symmetry may emerge at the quantum critical point (QCP). As the system is driven away from the QCP with a relevant perturbation, exotic physics may further emerge due to the strong renormalization of the almost infinite low-lying excitations [2]. The transverse-field Ising chain (TFIC) is a paradigmatic model [1], [2], [3]: when an Ising chain is tuned to its QCP by a magnetic field applied transverse to its Ising anisotropy, a central charge 1/2 conformal field theory emerges with corresponding scaling exponents falling into the class of Ising universality (Fig. 1) [3], [4]. Surprisingly, when it is further perturbed by a longitudinal field parallel to the Ising direction, the quantum E8 integrable model emerges — a massive relativistic quantum field theory containing eight massive E8 particles (Table S1 online). The physics of the model could be described by the scattering of the E8 particles as the maximal exceptional Lie E8 algebra [2], [5], [6]. Hence, exploring quantum E8 field theory can extend the frontier of quantum statistical field theory, and may even inspire the studies in high-energy physics.