Long-range phase order in two dimensionsand rainbow Goldstone mode under shear flow

 In April 2021, a post-doctoral researcher of Zhejiang University, Dr. Yuki Minami, and his collaborators published two papers on new phenomena of nonequilibrium systems in Physical Review Letters [1, 2].

 Nature exhibits various types of long-range order such as in crystalline solids, liquid crystals, ferromagnets, and Bose-Einstein condensates. Whereas the long-range ordered states are ubiquitous in the three-dimensional world, those associated with continuous symmetry breaking are forbidden in two-dimensional equilibrium system by the Mermin-Wagner theorem.

 Recently, the long-range phase order out of equilibrium attracts much attention. An intriguing example is the flocking behavior of living things such as birds and fishes. These are identified as spontaneous emergence of the polar or the phase order in nonequilibrium systems. A remarkable feature there is that it occurs even in two dimensions, even though it is prohibited in equilibrium systems.

 The aim of their study is to clarify how the long-range phase order emerges in two dimensions under a small nonequilibrium perturbation around equilibrium systems. They study a two-dimensional system that is driven into a nonequilibrium steady state by an infinitesimal shear flow. The Letter [1] is the first to show that such small nonequilibrium perturbation can cause the long-range order state in two dimensions. They have also shown that the long-range order originates from novel behaviors of gapless modes under the shear flow, which is named as rainbow Goldstone modes [2].

 These works were supported by the Zhejiang Provincial Natural Science Foundation Key Project (Grant No. LZ19A050001) and NSF of China (Grants No. 11975199 and 11674283).

References:

[1] H. Nakano, Y. Minami and S. Sasa, Physical Review Letters 126, 160604 (2021).

[2] Y. Minami, H. Nakano and Y. Hidaka, Physical Review Letters 126, 141601 (2021).