Superoperator structures and no-go theorems for dissipative quantum phase transitions

In the thermodynamic limit, steady states of open quantum many-body systems can undergo nonequilibrium phase transitions due to a competition between coherent and driven-dissipative dynamics. Here, we consider Markovian elucidate structures Liouville superoperator that generates time evolution. many cases interest, an operator-basis transformation bring Liouvillian into block-triangular form, making it possible assess its spectrum. The spectral gap sets asymptotic decay rate. structure be used bound gaps from below, showing that, in large class systems, dissipative are actually impossible convergence follows exponential temporal decay. Furthermore, when blocks on diagonal Hermitian, spectra obey Weyl ordering relations. results apply, for example, Davies generators quadratic also demonstrated various spin models.