Hidden Critical Points in the Two-Dimensional $O(n>2)$ model: Exact Numerical Study of a Complex Conformal Field Theory

Abstract

The presence of nearby conformal field theories (CFTs) hidden in the complex plane of the tuning parameter was recently proposed as an elegant explanation for the ubiquity of "weakly first-order" transitions in condensed matter and high-energy systems. In this work, we perform an exact microscopic study of such a complex CFT (CCFT) in the two-dimensional $O(n)$ loop model. The well-known absence of symmetry-breaking of the $O(n>2)$ model is understood as arising from the displacement of the non-trivial fixed points into the complex temperature plane. Thanks to a numerical finite-size study of the transfer matrix, we confirm the presence of a CCFT in the complex plane and extract the real and imaginary parts of the central charge and scaling dimensions. By comparing those with the analytic continuation of predictions from Coulomb gas techniques, we determine the range of validity of the analytic continuation to extend up to $n_g\approx 12.34$, beyond which the CCFT gives way to a gapped state. Finally, we propose a beta function which reproduces the main features of the phase diagram and which suggests an interpretation of the CCFT as a liquid-gas critical point at the end of a first-order transition line.

arXiv comment6 pages, 4 figures

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• The two upper critical dimensions of the Ising and Potts models
• Complex entanglement entropy for complex conformal field theory
• The Nordic-walking mechanism and its explanation of deconfined pseudocriticality from Wess-Zumino-Witten theory
• Pseudocriticality in antiferromagnetic spin chains
• Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts model
• Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model
• Asymptotic freedom, lost: Complex conformal field theory in the two-dimensional $O(N>2)$ nonlinear sigma model and its realization in Heisenberg spin chains