Loss of Asymptotic Freedom in the Two-Dimensional O(N) Nonlinear Sigma Model: Complex Conformal Field Theory and Realization in Heisenberg Spin Chains.

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 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 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≤2. The low-energy spectra also reveal a noninvertible symmetry inherited from the O(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.