Square-lattice J-Q models provide a sign-problem-free setting for probing the quantum phase transition between Néel antiferromagnets and columnar valence-bond solids. We analyze this transition through the scaling of Lee-Yang zeros, computed within stochastic series expansion quantum Monte Carlo by reweighting configurations sampled near criticality in the presence of complex source fields. Benchmark studies of the dimerized Heisenberg model and the checkerboard J-Q model validate the method, yielding stable $\mathrm{O}\left(3\right)$ critical scaling in the former and clear spacetime-volume scaling in the latter, as expected for a first-order transition. Applying the same analysis to the J-Q models, we find a pronounced and systematic drift of the leading-zero scaling with increasing system size, consistent with an extended pseudocritical regime. The Lee-Yang scaling implies an effective scaling dimension ${\mathrm{\Delta }}_{\varphi }$ of the $\mathrm{SO}\left(5\right)$ order-parameter field that decreases with size and is consistent with vanishing in the thermodynamic limit. Such behavior lies below the scalar unitarity bound of any unitary relativistic conformal field theory in $2+1$ dimensions and enforces inverse spacetime-volume scaling of the zeros, the hallmark of a first-order transition. These results support a weakly first-order interpretation of the Néel–VBS transition and establish the finite-size Lee-Yang zeros as a sensitive, symmetry-resolved diagnostic of pseudocriticality and transition order in the J-Q family.

Close

PrevNext

View figure in article

• Conformal field theory
• Quantum phase transitions
• Lee-Yang & Fisher zeroes
• Quantum Monte Carlo
• Spin lattice models