The two-dimensional $\mathrm{O}(\mathrm{N})$ nonlinear sigma model (NLSM) is asymptotically free for $N>2$: it exhibits neither a nontrivial fixed point nor spontaneous symmetry breaking. Here, we show that a nontrivial fixed point generically does exist in the complex coupling plane and is described by a complex conformal field theory (CCFT). This CCFT fixed point is generic in the sense that it has a single relevant singlet operator, and is thus expected to arise in any non-Hermitian model with $\mathrm{O}(\mathrm{N})$ symmetry upon tuning a single complex parameter. We confirm this prediction numerically by locating the CCFT at $N=3$ in two non-Hermitian spin-1 antiferromagnetic Heisenberg chains, and in a non-Hermitian spin-$1/2$ ladder, finding good agreement between the complex central charge and scaling dimensions and those obtained by analytic continuation of real fixed points from $N\le 2$. The low-energy spectra also reveal a noninvertible symmetry inherited from the $\mathrm{O}(\mathrm{N})$ loop model, realized as an emergent symmetry at the NLSM fixed point and exactly in the spin-1/2 ladder. We further construct a realistic Lindbladian for a spin-1 chain whose no-click dynamics are governed by the non-Hermitian Hamiltonian realizing the CCFT. Since the CCFT vacuum is the eigenstate with the smallest decay rate, the system naturally relaxes under dissipative dynamics toward a conformal field theory state, thus providing a route to preparing long-range entangled states through engineered dissipation.

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• Conformal field theory
• Critical phenomena
• Magnetism
• Open quantum systems
• Quantum criticality
• Non-Hermitian systems