Dynamical structure factors and excitation modes of the bilayer Heisenberg model

TL;DR

This paper investigates the dynamical spin structure factors and excitation modes of the bilayer Heisenberg model using advanced simulation and theoretical methods, revealing detailed spectral behaviors across quantum phase transitions.

Contribution

It combines multiple theoretical and numerical approaches to analyze the dynamical structure factors, identifying spectral features and modes near the quantum critical point in the bilayer Heisenberg model.

Findings

Distinct spectral contributions from Goldstone and triplon modes.

Continuous evolution of spectral features across the phase transition.

Identification of a marginally-damped amplitude mode near criticality.

Abstract

Using quantum Monte Carlo simulations along with higher-order spin-wave theory, bond-operator and strong-coupling expansions, we analyse the dynamical spin structure factor of the spin-half Heisenberg model on the square-lattice bilayer. We identify distinct contributions from the low-energy Goldstone modes in the magnetically ordered phase and the gapped triplon modes in the quantum disordered phase. In the antisymmetric (with respect to layer inversion) channel, the dynamical spin structure factor exhibits a continuous evolution of spectral features across the quantum phase transition, connecting the two types of modes. Instead, in the symmetric channel we find a depletion of the spectral weight when moving from the ordered to the disordered phase. While the dynamical spin structure factor does not exhibit a well-defined distinct contribution from the amplitude (or Higgs) mode in the ordered phase, we identify an only marginally-damped amplitude mode in the dynamical singlet structure factor, obtained from interlayer bond correlations, in the vicinity of the quantum critical point. These findings provide quantitative information in direct relation to possible neutron or light scattering experiments in a fundamental two-dimensional quantum-critical spin system.