Critical scaling in one-dimensional non-reciprocal matter

Abstract

Unveiling universal non-equilibrium scaling laws has been a central theme in modern statistical physics, with recent attention increasingly directed toward non-equilibrium phases that exhibit rich dynamical phenomena. A striking example arises in non-reciprocal systems, where asymmetric interactions between components lead to inherently dynamic phases and unconventional criticality near a critical exceptional point (CEP), where the criticality arises from the coalescence of collective modes with an existing Nambu-Goldstone mode. However, the scaling behavior that emerges in this system with full consideration of many-body effects and stochastic noise remains largely elusive. Here, we establish a dynamical scaling law in a generic one-dimensional (1D) stochastic non-reciprocal $O(2)$-symmetric system. Through large-scale simulations, we uncover a new non-equilibrium scaling in the vicinity of the CEP, distinct from any previously known equilibrium or non-equilibrium universality classes. We report an anomalously large roughening exponent $\alpha_{\rm CEP}=1.35(5)$, which is to be compared with those of simple diffusion $\alpha_{\rm EW}=1/2$. In regimes where the system breaks into domains with opposite chirality and spatiotemporal vortices inevitably emerge, we find that fluctuations are strongly suppressed, leading to a logarithmic scaling as a function of system size $L$ that manifests a short-range correlation. This work elucidates the beyond-mean-field dynamics of non-reciprocal matter, thereby shedding light on the exploration of criticality in non-reciprocal phase transition across diverse physical contexts, from active matter and driven quantum systems to biological pattern formation and non-Hermitian physics.