Spin-Peierls instability of deconfined quantum critical points

Deconfined quantum critical points (DQCPs) are putative phase transitions beyond the Landau paradigm with emergent fractionalized degrees of freedom. The original example of a DQCP is the spin-$\frac{1}{2}$ quantum antiferromagnet on the square lattice which features a second-order transition between valence bond solid (VBS) and N\'eel order. The VBS order breaks a lattice symmetry, and the corresponding VBS order parameter may couple to lattice distortion modes (phonons) at appropriate momenta. We investigate a field-theoretic description of the DQCP in the presence of such a spin-lattice coupling. We show that treating phonons as classical lattice distortions leads to a relevant monopole-phonon interaction inducing an instability towards a distorted lattice by an analogous mechanism to the spin-Peierls instability in one dimension. Consequently, there is a breakdown of the DQCP which generally becomes a strong first-order transition. Taking into account the full quantum nature of the phonons, we argue that the continuous DQCP persists above a critical phonon frequency. Lastly, we comment on the connection to general gapless, deconfined gauge theories.