Roughening dynamics of quantum interfaces

The roughening transition, known from three dimensional classical spin systems, describes how fluctuations of interfaces transition from being bounded to scaling extensively with the system size after crossing the characteristic roughening temperature. We explore signatures of such phenomena in the dynamics of domain walls in the two dimensional quantum Ising model, where we observe pre-thermal steady states in their evolution well beyond the perturbative limit using Tree Tensor Networks. We formulate an effective model of the interface, which captures qualitative features of a roughening transition. Most notably, it exhibits a Berezinskii–Kosterlitz–Thouless quantum phase transition from smooth to rough interfaces, whose signatures extend to finite temperatures. These findings can be related to the observed slow thermalization in the full model, opening the way to a better understanding of pre-thermalization effects in interface dynamics, which can be easily implemented and tested in experimental setups such as Rydberg atom experiments.