2026/01/31 by Anonymous, Christopher Yang, Thomas Scaffidi
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Photonic Systems #Quantum Mechanics and Non-Hermitian Physics #cond-mat.stat-mech #cond-mat.str-el #hep-th #quant-ph
paper · pdf · doi:10.1103/6tsl-d9kn
openalex publication_date 2026/06/22 · openalex created_date 2026/06/23 · openalex updated_date 2026/07/31
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. 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.