Dimerized Phase and Transitions in a Spatially Anisotropic Square Lattice Antiferromagnet

We investigate the spatially anisotropic square lattice quantum antiferromagnet. The model describes isotropic spin-$1/2$ Heisenberg chains (exchange constant $J$) coupled antiferromagnetically in the transverse ($J_{\perp }$) and diagonal ($J_{\times }$), with respect to the chain, directions. Classically, the model admits two ordered ground states–with antiferromagnetic and ferromagnetic interchain spin correlations–separated by a first-order phase transition at $J_{\perp }=2J_{\times }$. We show that in the quantum model this transition splits into two, revealing an intermediate quantum-disordered columnar dimer phase, both in two dimensions and in a simpler two-leg ladder version. We describe quantum-critical points separating this spontaneously dimerized phase from classical ones.

Figure 1

Phase diagram of the frustrated ladder. Line AB marks the parameters corresponding to the lattice model.

Figure 2

Phase diagram of the two-dimensional model. Solid (dashed) lines denote phase boundaries of the quantum (classical) model.