Asymptotic freedom, lost: Complex conformal field theory in the two-dimensional O(N>2) nonlinear sigma model and its realization in the spin-1 Heisenberg chain

The two-dimensional O(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 textit{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 O(N) symmetry upon tuning a single complex parameter. We confirm this prediction numerically by locating the CCFT at N = 3 in a non-Hermitian spin-1 antiferromagnetic Heisenberg chain, finding good agreement between the complex central charge and scaling dimensions and those obtained by analytic continuation of real fixed points from Nleq 2. 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 CFT state, thus providing a route to preparing long-range entangled states through engineered dissipation.