Cascade of singularities in the spin dynamics of a perturbed quantum critical Ising chain

Abstract

When the quantum critical transverse-field Ising chain is perturbed by a longitudinal field, a quantum integrable model emerges in the scaling limit with massive excitations described by the exceptional $E_8$ Lie algebra. Using the corresponding analytical form factors of the quantum $E_8$ integrable model, we systematically study the spin dynamic structure factor of the perturbed quantum critical Ising chain, where particle channels with total energy up to 5$m_1$ ($m_1$ being the mass of the lightest $E_8$ particle) are exhausted. In addition to the significant single-particle contributions to the dynamic spectrum, each two-particle channel with different masses is found to exhibit an edge singularity at the threshold of the total mass and decays with an inverse square root of energy, which is attributed to the singularity of the two-particle density of states at the threshold. The singularity is absent for particles with equal masses due to a cancellation mechanism involving the structure of the form factors. As a consequence, the dynamic structure factor displays a cascade of bumping peaks in the continuum region with clear singular features which can serve as a solid guidance for the material realization of the quantum $E_8$ model.

arXiv comment12 pages, 8 figures

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Cited by in corpus (11)

• Duality and Form Factors in the Thermally Deformed Two-Dimensional Tricritical Ising Model
• Magnetic excitations in the one-dimensional Heisenberg-Ising model with external fields and their experimental realizations
• Local dynamics and thermal activation in the transverse-field Ising chain
• Spin dynamics of the $E_8$ particles
• Magnetization oscillations in a periodically driven transverse field Ising chain
• Truncated string state space approach and its application to nonintegrable spin-$\frac{1}{2}$ Heisenberg chain
• Singular transport in non-equilibrium strongly internal-coupled 1D tilted field spin-1/2 chain
• Spin dynamics and dark particle in a weak-coupled quantum Ising ladder with ${\mathcal{D}}_8^{(1)}$ spectrum
• Berry connection and quantum geometry in time-dependent systems with instantaneous quantum integrable field theory
• Emergent $D_8^{(1)}$ spectrum and topological soliton excitation in CoNb${}_2$O${}_6$
• Relativistic meson spectra on ion-trap quantum simulators