Superoperator structures and no-go theorems for dissipative quantum phase transitions
In the thermodynamic limit, the 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 systems and elucidate structures of the Liouville superoperator that generates the time evolution. In many cases of interest, an operator-basis transformation can bring the Liouvillian into a block-triangular form, making it possible to assess its spectrum. The spectral gap sets the asymptotic decay rate. The superoperator structure can be used to bound gaps from below, showing that, in a large class of systems, dissipative phase transitions are actually impossible and that the convergence to steady states follows an exponential temporal decay. Furthermore, when the blocks on the diagonal are Hermitian, the Liouvillian spectra obey Weyl ordering relations. The results apply, for example, to Davies generators and quadratic systems and are also demonstrated for various spin models.
Duke Scholars
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- 51 Physical sciences
- 49 Mathematical sciences
- 34 Chemical sciences
Citation
Published In
DOI
EISSN
ISSN
Publication Date
Volume
Issue
Related Subject Headings
- 51 Physical sciences
- 49 Mathematical sciences
- 34 Chemical sciences