Lee-Yang Zeros and Pseudocritical Drift in J-Q N\'eel-VBS Transitions

TL;DR

This paper uses Lee-Yang zeros analysis via quantum Monte Carlo to investigate the Nel-VBS transition in J-Q models, revealing signs of a weakly first-order transition and pseudocritical behavior.

Contribution

It introduces a Lee-Yang zeros scaling method to diagnose the order of quantum phase transitions in J-Q models, highlighting pseudocritical regimes and transition characteristics.

Findings

Lee-Yang zeros exhibit systematic drift with system size.

Effective scaling dimension decreases and approaches zero in the thermodynamic limit.

Results support a weakly first-order Nel-VBS transition.

Abstract

Square-lattice J-Q models provide a sign-problem-free setting for probing the quantum phase transition between N\'eel antiferromagnet and columnar valence-bond solid. 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 O(3) 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 of the SO(5) 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 N\'eel-VBS transition and establish finite-size Lee-Yang zeros as a sensitive, symmetry-resolved diagnostic of pseudocriticality and transition order in the J-Q family.