Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model

Abstract

Conformal symmetry, emerging at critical points, can be lost when renormalization group fixed points collide. Recently, it was proposed that after collisions, real fixed points transition into the complex plane, becoming complex fixed points described by complex conformal field theories (CFTs). Although this idea is compelling, directly demonstrating such complex conformal fixed points in microscopic models remains highly demanding. Furthermore, these concrete models are instrumental in unraveling the mysteries of complex CFTs and illuminating a variety of intriguing physical problems, including weakly first-order transitions in statistical mechanics and the conformal window of gauge theories. In this work, we have successfully addressed this complex challenge for the (1+1)-dimensional quantum $5$-state Potts model, whose phase transition has long been known to be weakly first-order. By adding an additional non-Hermitian interaction, we successfully identify two conjugate critical points located in the complex parameter space, where the lost conformality is restored in a complex manner. Specifically, we unambiguously demonstrate the radial quantization of the complex CFTs and compute the operator spectrum, as well as new operator product expansion coefficients that were previously unknown.

6+13 pages

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• Complex entanglement entropy for complex conformal field theory
• Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking
• Pseudocriticality in antiferromagnetic spin chains
• A Fuzzy Sphere Journey in Critical Phenomena
• Boundary Criticality of Complex Conformal Field Theory: A Case Study in the Non-Hermitian 5-State Potts Model
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Walking behavior induced by $\mathcal{P}\mathcal{T}$ symmetry breaking in a non-Hermitian $\mathrm{XY}$ model with clock anisotropy
• Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts 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