Signatures of Quantum Phase Transitions in Driven Dissipative Spin Chains

Abstract: Open driven quantum systems have defined a powerful paradigm of non-equilibrium phases and phase transitions; however, quantum phase transitions are generically not expected in this setting due to the decohering effect of dissipation. In this work, we show that a driven-dissipative quantum spin chain exhibits a peculiar sensitivity to the ground-state quantum phase transition. Specifically, we consider a quantum Ising model subject to bulk dissipation (at rate $\Gamma$) and show that, although the correlation length remains finite (hence no phase transition), it develops a pronounced peak close to the ground-state quantum critical point. While standard techniques seem to fail in this regime, we develop a versatile analytical approach that becomes exact with vanishing dissipation ($\Gamma \to 0$ but finite $\Gamma t$). On a technical level, our approach builds on previous work where the state of the system is described by a slowly evolving generalized Gibbs ensemble that accounts for the integrability of the Hamiltonian (described by free fermions) while treating dissipation perturbatively which leads to nontrivial, nonlinear equations for fermionic correlators. Finally, we demonstrate a kind of universality in that integrability-breaking perturbations of the Hamiltonian lead to the same behavior.