Quantum spin liquids may arise in frustrated magnets, where interactions lead to a competition of many different possible ground states. However, this competition also makes such frustrated systems highly susceptible to external perturbations. For example, the system may relieve some frustration by undergoing a lattice distortion which favours a magnetic (or trivial) ground state.

We have recently studied the impact of lattice distortion modes on U(1) Dirac spin liquids on a triangular lattice, which are believed to be described by a strongly coupled conformal field theory. Using a combination of field-theoretic arguments and numerical analysis, we find that they exhibit an instability towards undergoing lattice distortion with concomitant VBS ordering for infinitesimally weak couplings to a classical distortion field [1], constituting a (2+1)-dim. generalisation of the well-known spin-Peierls instability of (1+1)-dimensional spin chains. Remarkably, large-scale variational Monte Carlo simulations allow us to observe quantum-critical scaling near the instability [2]. Considering quantum distortion modes with a finite frequency protects the spin liquid from the instability up to some critical spin-lattice coupling.

Given the conceptual overlap and formally similar description, we have further shown that continous deconfined quantum critical points exhibit a similar instability upon introducing spin-lattice couplings, rendering the transition to be first-order [3].