Weak first-order pseudocriticality with approximate scale invariance has been observed in a variety of settings, including the intriguing case of deconfined criticality in $2+1$ dimensions. Recently, this has been interpreted as extremely slow flows (“walking behavior”) for real-valued couplings in proximity to a bona fide critical point with complex-valued couplings, described by a complex conformal field theory (CFT). Here we study an $\mathrm{SU}(N)$ generalization of the Heisenberg antiferromagnet, which is a familiar model for deconfined criticality in $2+1$ dimensions. We show that in $1+1$ dimensions the model is located near a complex CFT, whose proximity can be tuned as a function of $N$. We employ state-of-the-art quantum Monte Carlo simulations for continuous $N$ along with an improved loop estimator for the Rényi entanglement entropy based on a nonequilibrium work protocol. These techniques allow us to track the central charge of this model in detail as a function of $N$, where we observe excellent agreement with CFT predictions. Notably, this includes the region $N>2$, where the CFT moves into the complex plane and pseudocritical drifts enable us to recover the real part of the complex central charge with remarkable accuracy. Since the present model with $N=3$ is also equivalent to the spin-1 biquadratic model, our Letter sheds new light on the dimerized phase of the spin-1 chain, demonstrating that it is pseudocritical and proximate to a complex CFT.

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• Entanglement entropy
• Magnetism
• Quantum phase transitions
• Conformal field theory
• Critical phenomena