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.
Highlights
Understanding and manipulating dissipation effects in open quantum systems [1] is increasing in importance, due to its crucial role in designing new optical devices and performing quantum computation
We have proposed a mechanism for the occurrence of the dynamic critical phenomena that arise at the critical exceptional point (CEP), originated from the coalescence of the collective eigenmodes to the Goldstone mode
We showed that this peculiar property gives rise to anomalously giant phase fluctuations that diverge at d 4. It leads to the appearance of a sound mode that anomalously enhances the many-body correlation effects, which survive at exceptionally high spatial dimensions (d < 8)
Summary
Understanding and manipulating dissipation effects in open quantum systems [1] is increasing in importance, due to its crucial role in designing new optical devices and performing quantum computation. We propose a non-Hermitian-induced critical phenomenon activated by the thermal and dissipative noise that occurs at a many-body EP, which can arise in generic drivendissipative quantum many-body systems composed of coupled binary order parameters. Our previous work [29] has shown that driven-dissipative systems composed of two components exhibit a non-Hermitian phase transition with an end point of its phase boundary marked by a many-body EP (as schematically shown and demonstrated in Fig. 2), proposed as an interpretation of the phase transition observed in some polariton experiments in the U(1)-broken phase [30,31,32,33,34,35]) (the so-called “second threshold”).
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