Spin- 1 2 J 1 - J 2 Heisenberg model on a cross-striped square lattice

Using the coupled cluster method (CCM) we study the full (zero-temperature) ground-state (GS) phase diagram of a spin-half (s=12) J1-J2 Heisenberg model on a cross-striped square lattice. Each site of the square lattice has four nearest-neighbor exchange bonds of strength J1 and two next-nearest-neighbor (diagonal) bonds of strength J2. The J2 bonds are arranged so that the basic square plaquettes in alternating columns have either both or no J2 bonds included. The classical (s→∞) version of the model has four collinear phases when J1 and J2 can take either sign. Three phases are antiferromagnetic (AFM), showing so-called Néel, double Néel, and double columnar striped order, respectively, while the fourth is ferromagnetic. For the quantum s=12 model we use the three classical AFM phases as CCM reference states, on top of which the multispin-flip configurations arising from quantum fluctuations are incorporated in a systematic truncation hierarchy. Calculations of the corresponding GS energy, magnetic order parameter, and the susceptibilities of the states to various forms of valence-bond crystalline (VBC) order are thus carried out numerically to high orders of approximation and then extrapolated to the (exact) physical limit. We find that the s=12 model has five phases, which correspond to the four classical phases plus a new quantum phase with plaquette VBC order. The positions of the five quantum critical points are determined with high accuracy. While all four phase transitions in the classical model are first order, we find strong evidence that three of the five quantum phase transitions in the s=12 model are of continuous deconfined type.