Thomas Barthel (Duke U.)
Criticality and phase transitions in open quantum many-body systems
 
In the thermodynamic limit, the nonequilibrium steady states of open quantum many-body systems can undergo phase transitions due to the competition of unitary and driven-dissipative dynamics. We consider Markovian systems and elucidate structures of the Liouville super-operator that generates the dynamics. In many cases of interest, an operator basis transformation can bring the Liouvillian into block-triangular form, making it possible to assess its spectrum. The super-operator structure can be used to bound gaps, showing that, in a large class of systems, dissipative phase transitions are actually impossible and that the convergence to steady states is exponential [1].
A large class of translation-invariant fermionic and bosonic systems can be characterized almost completely -- "quadratic" systems, where the Hamiltonian is quadratic in the ladder operators, and the Lindblad operators are either linear or quadratic and Hermitian [2]. We find that one-dimensional systems with finite-range interactions cannot be critical, i.e., steady-state correlations necessarily decay exponentially. For the quasi-free case without quadratic Lindblad operators, we show that fermionic systems with short-range interactions are non-critical for any number of spatial dimensions and provide bounds on the correlation lengths. Quasi-free bosonic systems in d>1 dimensions can be critical. Lastly, we address the question of phase transitions finding that, for quadratic systems without symmetry constraints beyond particle-hole symmetries, all gapped Liouvillians belong to the same phase [3]. This extends to non-quadratic systems above an upper critical dimension.

[1] Y. Zhang and T. Barthel, "Criticality and phase classification for quadratic open quantum many-body systems", Phys. Rev. Lett. 129, 120401 (2022)
[2] T. Barthel and Y. Zhang, "Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems", arXiv:2112.08344, J. Stat. Mech. (2022)
[3] T. Barthel and Y. Zhang, "Super-operator structures and no-go theorems for dissipative quantum phase transitions", Phys. Rev. A 105, 052224 (2022)