Quantum-critical and dynamical properties of the XXZ bilayer with long-range interactions - Adelhardt, Patrick; Duft, Antonia; Schmidt, Kai Phillip (Physical Review B, 2025)
We study the XXZ square lattice bilayer model with antiferromagnetic nonfrustrating long-range interactions that decay as a power law with the distance. Employing large-scale high-order series expansions with classical Monte Carlo integration (pCUT+MC) about the limit of isolated Heisenberg dimers in the rung-singlet phase, we investigate the one-triplon dispersion and the corresponding spectral weight along the parameter axes of the long-range decay exponent and the XXZ anisotropy. By tuning the latter, we observe two extended regions of 3D XY and Ising universality as well as 3D Heisenberg critical exponents at the isotropic point. Along the decay exponent axis, we demonstrate mean-field behavior for strong long-range couplings, the aforementioned three universality classes for sufficiently weak interactions, and continuously varying critical exponents in between. Using extrapolations, we are able to determine the one-triplon dispersion in a quantitative fashion up to the quantum-critical breakdown of the rung-singlet phase. This allows us to extract the dynamical critical exponent 𝑧 as a function of the decay exponent, displaying a universal behavior. The detected 𝑧<1 for small decay exponents is in agreement with the expected properties of the anomalous Goldstone modes in the ordered phases with broken continuous symmetr
Keywords: Antiferromagnetism; Critical exponents; Goldstone bosons; Hard-core bosons; Long-range interactions; Magnons; Phase diagrams; Quantum criticality; Quantum phase transitions; Triplon; XY model; Quantum many-body systems; Square lattice; Heisenberg model; Linear spin wave theory; Monte Carlo methods; Perturbative methods; Series expansions & exact enumeration