Balázs Pozsgay
(Budapest)
 

In quantum many body systems symmetries lead to conservation laws, and if a specific system has exotic symmetries, then its dynamics will not be ergodic. We discuss a special phenomenon, where a quantum spin chain has exotic symmetries described by Matrix Product Operators. Such symmetries have been known to exist in integrable spin chains, where they are given by the commuting set of transfer matrices. However, in our case we find a non-commutative symmetry algebra in a non-integrable spin chain. This leads to exponentially large degeneracies, the breakdown of ergodicity and thermalization. The mechanism behind the symmetries seems to be new: it is related to the "hard rod deformation'' discovered recently, which is a general framework that was first seen specifically in the so-called folded XXZ model, which is integrable. However, the new models include non-integrable perturbations as well, meanwhile conserving the large symmetry algebra.