Finite-temperature valence-bond-solid transition of quantum spins in two dimensions

The $S=1/2$ Heisenberg model on the 2D square lattice with four- or six-neighbor spin interactions (JQ model) hosts a quantum phase transition between N\'eel and valence-bond-solid (VBS) ground states. The deconfined quantum critical (DQC) point, predicted by the theory of Senthil \emph{et al.}[1], may be realized in this model [2]. Here we study the finite-temperature phase transition between the VBS ($Z_4$ symmetry breaking) to the paramagnetic state. We find continuously changing exponents with the correlation-length exponent $\nu$ close to the Ising value far from the $T=0$ critical point, and diverging when the critical temperature $T_c \rightarrow 0^+$. This is in accord with the DQC theory, according to which the transition for $T_c \rightarrow 0^+ $ should approach a Kosterlitz-Thouless fixed point.\\[4pt] [1] T. Senthil, L. Balents, S. Sachdev, A. Vishwanath, and M. P. A. Fisher, Phys. Rev. B {\bf 70}, 144407 (2004).\\[0pt] [2] R. K. Kaul, R. G. Melko, A. W. Sandvik, arXiv:1204.5405.