Driven-dissipative Phase Transitions for Markovian Open Quantum Systems

Abstract

Due to recent experimental progress on highly controllable quantum systems, increasing attention has been paid to open quantum systems, where driving and dissipation can lead to undesirable decoherence but may also stabilize interesting states and lead to new physics. Theoretically speaking, the generator of the dynamics (called the Liouvillian) for open quantum systems is non-Hermitian, giving rise to phenomena not allowed in closed systems.This dissertation mainly studies dissipative phase transitions in open systems where the steady state undergoes a non-analytic change at the transition point. We apply various analytic methods to investigate different open many-body models. (i) We study open systems where the Liouvillian can be brought into a block-triangular form. This allows us to bound the spectral gap from below, showing that, in a large class of systems, dissipative phase transitions are impossible. (ii) We perform perturbative treatment to spin-1/2 systems with a large dephasing channel and study the non-Hermitian skin effect in such systems. (iii) We establish the solvability of quadratic open systems using the third-quantization technique. With this, we further investigate quadratic fermionic and bosonic systems respectively. We find that criticality is not allowed for quadratic fermionic systems while we find examples of bosonic criticality for d>=2 dimensional quadratic systems. We also establish a proposition stating that without symmetry constraints beyond invariance under single-particle basis and particle-hole transformations, all gapped Liouvillians belong to the same phase. (iv) We employ Keldysh field theory to study dissipative Bose-Einstein condensation. With the one-loop renormalization group calculation, we elucidate the universality class to which this phase transition belongs. (v) We study the mathematical structure of the Liouvillian and establish an algebraic condition for the irreducibility of the Liouvillian. Irreducibility will lead to the uniqueness and faithfulness of the steady state.