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

• Main Authors: D'Emidio, Jonathan, Eberharter, Alexander A, Läuchli, Andreas M
• Format: Journal Article
• Language: English
• Published: 22-09-2023
• Subjects: Physics - Strongly Correlated Electrons
• DOI: 10.48550/arxiv.2106.15462

SciPost Phys. 15, 061 (2023) 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 $Q$-state
Potts models, where the nature of the transition is continuous for $Q\leq4$ and
turns (weakly) first order for $Q>4$, 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 $S=1/2$ N\'eel to valence
bond solid transition in two dimensions, focusing on the square lattice $J$-$Q$
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.