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

TL;DR

This paper demonstrates the existence of complex conformal fixed points in a non-Hermitian quantum 5-state Potts model, restoring conformality in a complex parameter space and computing the associated operator spectrum.

Contribution

It provides the first microscopic demonstration of complex conformal fixed points in a non-Hermitian quantum model, including spectral and operator data.

Findings

Identification of conjugate critical points in complex parameter space

Restoration of conformality via complex fixed points

Computation of operator spectrum and OPE coefficients

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.