Thermal valence-bond-solid transition of quantum spins in two dimensions

We study the S = 1/2 Heisenberg (J) model on the two-dimensional (2D) square lattice in the presence of additional higher-order spin interactions (Q) which lead to a valence-bond-solid (VBS) ground state. Using quantum Monte Carlo simulations, we analyze the thermal VBS transition. We find continuously varying exponents, with the correlation-length exponent nu close to the Ising value for large Q/J and diverging when Q/J approaches the quantum-critical point (the critical temperature T-c -> 0). We identify the transition with a class of conformal field theories with charge c = 1 and critical exponents varying between those of the 2D Ising model and the Kosterlitz-Thouless (KT) fixed point. We find explicit evidence for KT physics by studying the emergence of U(1) symmetry of the order parameter at T = T-c when T-c -> 0.