Signatures of Quantum Phase Transitions in Driven Dissipative Spin Chains

TL;DR

This paper investigates how quantum phase transition signatures manifest in driven dissipative spin chains, revealing peaks in correlation length near critical points and establishing a universal behavior across different models.

Contribution

It develops an analytical approach to identify quantum critical signatures in open driven quantum systems with dissipation, bridging the gap between equilibrium and nonequilibrium phase transition analysis.

Findings

Correlation length peaks near quantum critical points.

Universal behavior in integrability-breaking perturbations.

Steady states resemble quench dynamics in the zero dissipation limit.

Abstract

Open driven quantum systems have defined a powerful paradigm of nonequilibrium phases and phase transitions; however, quantum phase transitions are generically not expected in this setting due to the decohering effect of dissipation. In this Letter, 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 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 while treating dissipation perturbatively. Finally, we demonstrate a kind of universality in that integrability-breaking perturbations of the Hamiltonian lead to the same behavior. To this end, we first show that the steady state of a chaotic Ising Hamiltonian under local Markovian dissipation that preserves the Ising symmetry, and in the limit $\Gamma \to 0$, is identical to that of quench dynamics in the absence of dissipation. This intriguing connection then allows us to draw on recent findings about quantum phase transition signatures in quench dynamics.