Dynamical scaling at critical exceptional points

In conventional critical phenomena, the slow and long-distance fluctuations are provided by the softening of a massive mode. Recently, a new class of critical phenomena driven instead by the coalescence of the collective modes to the Goldstone mode were found to occur in the steady state of open binary condensates [1] and in non-reciprocally interacting many-body systems [2]. Surprisingly, at this “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 difficult to determine the scaling exponents in realistic spatial dimensions with standard analytical techniques, due to the anomalously enhanced many-body effects. In this work, we perform a direct numerical study on the one-dimensional binary condensates described by the noisy driven-dissipative Gross-Pitaevskii equations. We found a strong evidence of anomalous large fluctuations near the CEP, as well as a surprisingly large many-body correction to the roughening exponent that strongly suppress these fluctuations.

[1] R. Hanai and P. B. Littlewood, Phys. Rev. Research 2, 033018 (2020).
[2] M. Fruchart, R. Hanai, P. B. Littlewood, and V. Vitelli, arXiv:2003.13176(2020).