Critical fluctuations in one-dimensional non-reciprocal matter

The celebrated Landau theory successfully describes the generic qualitative features of equilibrium phase transitions. However, this framework fails to capture the dynamical phases and critical scaling of non-equilibrium phase transitions influenced by stochastic noise. A particularly intriguing class of nonequilibrium phase transitions is the so-called non-reciprocal phase transitions, which arises generically in active systems with multiple order parameters [1,2]. Their transition is characterized by the coalescence of the collective modes to the Nambu-Goldstone mode associated with a spectral singularity called the critical exceptional point (CEP). Although it has been theoretically predicted that CEPs exhibit anomalously giant fluctuations [1] that gives rise to fluctuation-induced discontinuous transitions at d=3 dimensions [3], the role of many-body correction from nonlinear effects at lower dimensions has remained elusive.

In this work, we numerically investigate a fluctuating hydrodynamics of one-dimensional non-reciprocal system with O(2) symmetry. Our results confirm the emergence of giant critical fluctuations near CEPs, revealing a new universality class with precisely extracted exponents. Additionally, we uncover the emergence of persistent dynamical patterns characterized by space-time vortex lattice and distinctive logarithmic scaling with system size. Both CEP scalings and the dynamical pattern scaling contrast sharply with the typical Edward-Wilkinson (EW) scaling in Gaussian diffusive systems. These results open new avenues for exploring criticality and pattern formation in the dynamical phase transitions in non-reciprocal matter.

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

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

[3] C. P. Zelle, R. Daviet, A. Rosch, and S. Diehl, Phys. Rev. X 14, 021052 (2024).