Effect of acoustic phonons on quantum criticality

We study the fate of quantum criticality in a spin system coupled to gapless phonons. In one dimension, a recent study based on renormalization group (RG) analysis and density matrix renormalization group (DMRG) calculations reveals the possibility of the transition to remain second-order or driven to first-order, depending on the ratio of velocities of the spins and the phonons. Our goal is to understand how the coupling affects the transition in higher dimensions. We did a perturbative RG analysis of the Φ⁴ theory coupled to acoustic phonons, using an ε expansion near (3+1) dimensions. Our analysis is supplemented by a Quantum Monte Carlo simulation of the coupled system in two and three dimensions.