Quantum integrability vs experiments: correlation functions and dynamical structure factors

Integrable Quantum Field Theories can be solved exactly using bootstrap techniques based on their elastic and factorisable S-matrix. While knowledge of the scattering amplitudes reveals the exact spectrum of particles and their on-shell dynamics, the expression of the matrix elements of the various operators allows the reconstruction of off-shell quantities such as two-point correlation functions with a high level of precision. In this review, we summarise results relevant to the contact point between theory and experiment providing a number of quantities that can be computed theoretically with great accuracy. We concentrate on universal amplitude ratios which can be determined from the measurement of generalised susceptibilities, and dynamical structure factors, which can be accessed experimentally e.g. via inelastic neutron scattering or nuclear magnetic resonance. Besides an overview of the subject and a summary of recent advances, we also present new results regarding generalised susceptibilities in the tricritical Ising universality class.

Automated summary

In this review, the author discusses the solvability of Integrable Quantum Field Theories using bootstrap techniques based on their elastic and factorisable S-matrix. The author emphasizes the importance of knowledge of scattering amplitudes and matrix elements in determining the exact spectrum of particles and their off-shell dynamics. The article also explores the calculation of universal amplitude ratios and dynamical structure factors, which can be experimentally accessed through methods like inelastic neutron scattering or nuclear magnetic resonance. Additionally, new results regarding generalized susceptibilities in the tricritical Ising universality class are presented.