Dynamical scaling at critical exceptional points

In the many-body context, exceptional points (EPs), spectral singularities where eigenmodes completely coalesce, can possess similar properties to critical points due to the occurrence of gap closure [1,2]. This provides a new class of nonequilibrium phase transitions in generic nonequilibrium systems with spontaneously broken continuous symmetry characterized by coupled multiple-order parameters [2]. Surprisingly, at the critical exceptional point (CEP), it was shown that the critical fluctuations become anomalous giant (which diverges at d≤4) compared to the conventional case (which diverges at d≤2) [1]. However, it was found difficult to investigate the dynamical scaling in realistic spatial dimensions with standard analytical techniques, due to the anomalously enhanced many-body interaction effects. In our work, we perform a direct numerical study of driven many-body systems that exhibit CEPs. We found strong evidence of anomalous large long-time fluctuations as well as novel transient behaviors near the CEP.



[1] R. Hanai and P. B. Littlewood, Phys. Rev. Research 2, 033018 (2020).

[2] M. Fruchart, R. Hanai, P. B. Littlewood, and V. Vitelli, Nature 592, 363–369 (2021)