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

TL;DR

This paper investigates the spin dynamics of a perturbed quantum critical Ising chain, revealing cascade singularities in the dynamic structure factor linked to the underlying E8 integrable model, with implications for material realization.

Contribution

It provides a systematic analysis of the spin dynamic structure factor in the E8 quantum integrable model, highlighting the cascade of singularities and their physical origins.

Findings

Two-particle channels exhibit edge singularities at total mass thresholds.

Singularities decay as inverse square root of energy, except for equal-mass particles.

Dynamic structure factor shows a cascade of bumping peaks with distinct singular features.

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.