Peierls-Like Transition Induced by Frustration in a Two-Dimensional Antiferromagnet

We show that the introduction of frustration into the spin- $1/2$ two-dimensional (2D) antiferromagnetic Heisenberg model on a square lattice via a next-nearest-neighbor exchange interaction can lead to a Peierls-like transition, from a tetragonal to an orthorhombic phase, when the spins are coupled to adiabatic phonons. The two different orthorhombic ground states define an Ising order parameter, which is expected to lead to a finite temperature transition. Implications for ${\mathrm{Li}}_2{\mathrm{VOSiO}}_4$, the first realization of that model, will be discussed.