Diagnosing weakly first-order phase transitions by coupling to order parameters

The hunt for exotic quantum phase transitions described by emergent fractionalized degrees of freedom coupled to gauge fields requires a precise determination of the fixed point structure from the field theoretical side, and an extreme sensitivity to weak first-order transitions from the numerical side. Addressing the latter, we revive the classic definition of the order parameter in the limit of a vanishing external field at the transition. We demonstrate that this widely understood, yet so far unused approach provides a diagnostic test for first-order versus continuous behavior that is distinctly more sensitive than current methods. We first apply it to the family of Q Q -state Potts models, where the nature of the transition is continuous for Q≤4 Q ≤ 4 and turns (weakly) first order for Q>4 Q > 4 , using an infinite system matrix product state implementation. We then employ this new approach to address the unsettled question of deconfined quantum criticality in the S=1/2 S = 1 / 2 Néel to valence bond solid transition in two dimensions, focusing on the square lattice J J - Q Q model. Our quantum Monte Carlo simulations reveal that both order parameters remain finite at the transition, directly confirming a first-order scenario with wide reaching implications in condensed matter and quantum field theory.