***Paper*** Stable topological order in three dimensions


In a new Phys. Rev. B paper, we show that topological order in 3D has tensor network descriptions stable against arbitrary perturbations.

Topologically ordered systems ­– that is, system which exhibit ordering in non-trivial global quantum correlations – exhibit unconventional physical phenomena and are promising candidates for the realization of quantum memories and computers. This makes their analytical modelling and numerical simulation an important task.

Tensor network form a powerful way to describe topological order starting from local correlations. However, in two dimensions (2D), their topological order has been found to be unstable under even the smallest perturbation of the underlying tensor. It has been argued that this instability is closely linked to the instability of topological order in 2D under finite temperature.

In a new paper in the Physical Review B, a team around Dominic Williamson and our group leader Norbert Schuch has shown that in three dimensions, tensor networks can described in ways which are stable under arbitrary local perturbations. This provides new means to reliably model topological in particular in numerical simulations, without the need to manually impose specific symmetries which had been hitherto believed to be directly linked to topological order. This effect is all the more surprising since in order to be stable against thermal fluctuations, one has to go even another one dimension higher and consider four-dimensional topological models.

More details can be found in the paper at Physical Review B or on the arXiv.

This work has received support through the ERC grant SEQUAM.