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

• URL: http://arxiv.org/abs/2601.02459v1
• Date: Mon, 05 Jan 2026 19:00:00 GMT
• Title: 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
• Authors: Christopher Yang, Thomas Scaffidi,
• Abstract summary: We show that a nontrivial fixed point generically does exist in the $textitcomplex$ coupling plane and is described by a complex conformal field theory (CCFT)<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\textit{complex}$ 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 $N\leq 2$. 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.

Related papers

• From QED$_3$ to Self-Dual Multicriticality in the Fradkin-Shenker Model [0.0]
  We consider the Fradkin-Shenker $mathbb Z$ gauge-Higgs lattice model in 2+1 dimensions.<n>Its phase diagram contains a multicritical CFT with gapless, mutually non-local electric and magnetic particles.<n>We compute the scaling dimensions of some operators using a large-$N_f$ expansion and find agreement with the emergent selection rules.
  arXiv  Detail & Related papers  (2026-02-26T19:00:00Z)
• $\mathcal{PT}$-like phase transitions from square roots of supersymmetric Hamiltonians [0.0]
  We introduce a general framework for realizing $mathcalPT$-like phase transitions in non-Hermitian systems.<n>This work uncovers new links between non-Hermitian physics and supersymmetry.
  arXiv  Detail & Related papers  (2025-11-16T23:38:51Z)
• Theta-term in Russian Doll Model: phase structure, quantum metric and BPS multifractality [45.88028371034407]
  We investigate the phase structure of the deterministic and disordered versions of the Russian Doll Model (RDM)<n>We find the pattern of phase transitions in the global charge $Q(theta,gamma)$, which arises from the BA equation.<n>We conjecture that the Hamiltonian of the RDM model describes the mixing in particular 2d-4d BPS sector of the Hilbert space.
  arXiv  Detail & Related papers  (2025-10-23T17:25:01Z)
• Field digitization scaling in a $\mathbb{Z}_N \subset U(1)$ symmetric model [0.0]
  We propose to analyze field digitization by interpreting the parameter $N$ as a coupling in the renormalization group sense.<n>Using effective field theory, we derive generalized scaling hypotheses involving the FD parameter $N$.<n>We analytically prove that our calculations for the 2D classical-statistical $mathbbZ_N$ clock model are directly related to the quantum physics in the ground state of a (2+1)D $mathbbZ_N$ lattice gauge theory.
  arXiv  Detail & Related papers  (2025-07-30T18:00:02Z)
• Meson spectroscopy of exotic symmetries of Ising criticality in Rydberg atom arrays [39.58317527488534]
  Coupling two Ising chains in a ladder leads to an even richer $mathcalD(1)_8$ symmetries.<n>Here, we probe these emergent symmetries in a Rydberg atom processing unit, leveraging its geometry to realize both chain and ladder configurations.
  arXiv  Detail & Related papers  (2025-06-26T14:19:30Z)
• Learning single-index models via harmonic decomposition [21.065469907392643]
  We study the problem of learning single-index models, where the label $y in mathbbR$ depends on the input $boldsymbolx in mathbbRd$ only through an unknown one-dimensional projection.<n>We introduce two families of estimators -- based on tensor unfolding and online SGD -- that respectively achieve either optimal sample complexity or optimal runtime.
  arXiv  Detail & Related papers  (2025-06-11T15:59:53Z)
• Non-stabilizerness of Neural Quantum States [41.94295877935867]
  We introduce a methodology to estimate non-stabilizerness or "magic", a key resource for quantum complexity, with Neural Quantum States (NQS)<n>We study the magic content in an ensemble of random NQS, demonstrating that neural network parametrizations of the wave function capture finite non-stabilizerness besides large entanglement.
  arXiv  Detail & Related papers  (2025-02-13T19:14:15Z)
• Universal non-Hermitian flow in one-dimensional PT-symmetric quantum criticalities [5.402334522977581]
  We study the finite-size scaling of the energy of non-Hermitian Su-Schrieffer-Heeger model with parity and time-reversal symmetry. We find that under open boundary condition (OBC), the energy scaling $E(L)sim c/L$ reveals a negative central charge $c=-2$ at the non-Hermitian critical point. The scaling function demonstrates distinct behaviors at topologically non-trivial and trivial sides of critical points.
  arXiv  Detail & Related papers  (2024-05-02T18:02:13Z)
• Nonlinear sigma models for monitored dynamics of free fermions [0.0]
  We derive descriptions for measurement-induced phase transitions in free fermion systems. We use the replica trick to map the dynamics to the imaginary time evolution of an effective spin chain. This is a nonlinear sigma model for an $Ntimes N$ matrix, in the replica limit $Nto 1$.
  arXiv  Detail & Related papers  (2023-02-24T18:56:37Z)
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors [7.371841894852217]
  Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena. We introduce an interesting quantity (denoted as $eta$) as a new variant of the Petermann factor to measure non-unitarity.
  arXiv  Detail & Related papers  (2022-08-31T16:24:03Z)
• A New Look at the $C^{0}$-formulation of the Strong Cosmic Censorship Conjecture [68.8204255655161]
  We argue that for generic black hole parameters as initial conditions for Einstein equations, the metric is $C0$-extendable to a larger Lorentzian manifold. We prove it violates the "complexity=volume" conjecture for a low-temperature hyperbolic AdS$_d+1$ black hole dual to a CFT living on a ($d-1$)-dimensional hyperboloid $H_d-1$.
  arXiv  Detail & Related papers  (2022-06-17T12:14:33Z)
• Duality, Criticality, Anomaly, and Topology in Quantum Spin-1 Chains [15.795926248847026]
  We argue that a model with self-duality (i.e., invariant under $U_textKT$) is natural to be at a critical or multicritical point. In particular, when $H$ is the Hamiltonian of the spin-1 antiferromagnetic Heisenberg chain, we prove that the self-dual model $H + U_textKT$ is exactly equivalent to a gapless spin-$1/2$ XY chain.
  arXiv  Detail & Related papers  (2022-03-29T17:50:16Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• Tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $\sigma$-model with $\theta=\pi$ term [17.494746371461694]
  We perform a tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $sigma$-model with $theta=pi$ term. Within the Hamiltonian formulation, this field theory emerges as the finite-temperature partition function of a modified quantum rotor model decorated with magnetic monopoles.
  arXiv  Detail & Related papers  (2021-09-23T12:17:31Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.