# Critical fluctuations at a many-body exceptional point

## TL;DR

This paper uncovers a new type of critical phenomena in driven-dissipative many-body systems caused by a non-Hermitian exceptional point, leading to giant phase fluctuations and a novel universality class beyond traditional classifications.

## Contribution

It introduces the concept of a critical exceptional point in many-body systems, revealing a new universality class and strong many-body effects driven by non-Hermitian physics.

## Key findings

- Giant phase fluctuations diverge at spatial dimensions d ≤ 4.
- A strong-coupling fixed point exists at dimensions up to d < 8.
- A sound mode appears at the critical exceptional point despite dissipation.

## Abstract

Critical phenomena arise ubiquitously in various context of physics, from condensed matter, high energy physics, cosmology, to biological systems, and consist of slow and long-distance fluctuations near a phase transition or critical point. Usually, these phenomena are associated with the softening of a massive mode. Here we show that a novel, non-Hermitian-induced mechanism of critical phenomena that do not fall into this class can arise in the steady state of generic driven-dissipative many-body systems with coupled binary order parameters such as exciton-polariton condensates and driven-dissipative Bose-Einstein condensates in a double-well potential. The criticality of this ``critical exceptional point'' is attributed to the coalescence of the collective eigenmodes that convert all the thermal-and-dissipative-noise activated fluctuations to the Goldstone mode, leading to anomalously giant phase fluctuations that diverge at spatial dimensions $d\le 4$. Our dynamic renormalization group analysis shows that this gives rise to a strong-coupling fixed point at dimensions as high as $d<8$ associated with a new universality class beyond the classification by Hohenberg and Halperin, indicating how anomalously strong the many-body corrections are at this point. We find that this anomalous enhancement of many-body correlation is due to the appearance of a sound mode at the critical exceptional point despite the system's dissipative character.