Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry

TL;DR

This paper provides experimental evidence of emergent E8 symmetry in a quantum Ising chain, revealing complex quantum behaviors near the critical point through precise magnetic field tuning and spin excitation analysis.

Contribution

It experimentally demonstrates the emergence of E8 symmetry in a real quantum Ising chain, confirming long-standing theoretical predictions.

Findings

Observation of a fine structure with two sharp low-energy modes

Approach of mode ratio to the golden mean as predicted for E8 spectrum

Transition of spin excitations from kink pairs to spin-flips

Abstract

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 8 particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by tuning the quasi-one-dimensional Ising ferromagnet CoNb2O6 through its critical point using strong transverse magnetic fields. The 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 as predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviours.