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

Abstract

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 $N\le 2$. 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.

10 pages, 7 figures + Supplemental Materials

References in corpus (67)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Geometric and Renormalized Entropy in Conformal Field Theory
• Non-Hermitian Physics
• A Rydberg Quantum Simulator
• Preparation of Entangled States by Quantum Markov Processes
• Keldysh Field Theory for Driven Open Quantum Systems
• Deconfined quantum critical points: symmetries and dualities
• Entanglement transition in a monitored free fermion chain -- from extended criticality to area law
• Dynamical Critical Phenomena in Driven-Dissipative Systems
• Conformality Lost
• Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
• Walking, Weak first-order transitions, and Complex CFTs
• Parity effects in the scaling of block entanglement in gapless spin chains
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
• Entanglement and purification transitions in non-Hermitian quantum mechanics
• Realising the Symmetry-Protected Haldane Phase in Fermi-Hubbard Ladders
• Emergent conformal symmetry in non-unitary random dynamics of free fermions
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition
• Dense loops, supersymmetry, and Goldstone phases in two dimensions
• A theory of deconfined pseudo-criticality
• Entanglement in non-unitary quantum critical spin chains
• Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain
• Dynamics and universality in noise driven dissipative systems
• Measurements conspire nonlocally to restructure critical quantum states
• Exceptional Bound States and negative Entanglement Entropy
• Nonlinear sigma models for monitored dynamics of free fermions
• Monte Carlo renormalization group study of the Heisenberg and XY antiferromagnet on the stacked triangular lattice and the chiral ${\varphi }^4$ model
• A spin chain model with non-Hermitian interaction: The Ising quantum spin chain in an imaginary field
• Emergence and spontaneous breaking of approximate O(4) symmetry at a weakly first-order deconfined phase transition
• Universality in driven open quantum matter
• Disordered monitored free fermions
• Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law
• Detecting signals of weakly first-order phase transitions in two-dimensional Potts models
• Rényi entropies and negative central charges in non-Hermitian quantum systems
• Measurement-altered Ising quantum criticality
• Phase diagram of the frustrated spin ladder
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Symmetry-resolved entanglement in critical non-Hermitian systems
• Dimerization transitions in spin-1 chains
• Frustration and Multicriticality in the Antiferromagnetic Spin-1 Chain
• Conformality Loss, Walking, and 4D Complex Conformal Field Theories at Weak Coupling
• Entanglement Entropy of Non-Hermitian Free Fermions
• Holographic Complex Conformal Field Theories
• Two-dimensional O(n) models and logarithmic CFTs
• Shadow of complex fixed point: Approximate conformality of Q>4 Potts model
• Global symmetry and conformal bootstrap in the two-dimensional $O(n)$ model
• Diagnosing weakly first-order phase transitions by coupling to order parameters
• Vaporization dynamics of a dissipative quantum liquid
• Complex fixed points of the non-Hermitian Kondo model in a Luttinger liquid
• An optimal dissipative encoder for the toric code
• Spaces of states of the two-dimensional O(n) and Potts models
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• Entanglement Transition due to particle losses in a monitored fermionic chain
• Creating and controlling exceptional points of non-Hermitian Hamiltonians via homodyne Lindbladian invariance
• Constructing the spin-1 Haldane phase on a qudit quantum processor
• Logarithmic entanglement scaling in dissipative free-fermion systems
• Hidden Critical Points in the Two-Dimensional $O(n>2)$ model: Exact Numerical Study of a Complex Conformal Field Theory
• Contrasting pseudo-criticality in the classical two-dimensional Heisenberg and ${\mathrm{RP}}^2$ models: zero-temperature phase transition versus finite-temperature crossover
• Unitarity of Symplectic Fermion in $\alpha$-vacua with Negative Central Charge
• Complex entanglement entropy for complex conformal field theory
• Driven Non-Unitary Dynamics of Quantum Critical Systems
• Conformal symmetry in quasi-free Markovian open quantum systems
• Pseudocriticality in antiferromagnetic spin chains
• On currents in the $O(n)$ loop model