Non-Equilibrium Phase Transition in a Boundary-Driven Dissipative Fermionic Chain

We demonstrate that a boundary-localized periodic (Floquet) drive can induce nontrivial long-range correlations in a non-interacting fermionic chain which is additionally subject to boundary dissipation. Surprisingly, we find that this phenomenon occurs even when the corresponding isolated bulk is in a trivial gapped phase with exponentially decaying correlations. We argue that this boundary-drive induced non-equilibrium transition (as witnessed through the correlation matrix) is driven by a resonance mechanism whereby the drive frequency bridges bulk energy gaps, allowing boundary-injected particles and holes to propagate and mediate long-range correlations into the bulk. We also numerically establish that when the drive bridges a particle-hole gap, the induced long-range order scales as a power law with the bulk pairing potential ($χ\sim γ^2$). Our results highlight the potential of localized coherent driving for generating macroscopic order in open quantum systems.

💡 Research Summary

In this work the authors study a minimal open‑quantum‑system model consisting of two non‑interacting Kitaev chains (labeled by spin ↑ and ↓) that are coupled only at their first site by a monochromatic, time‑periodic drive. The static Hamiltonian of each chain contains hopping (tσ), superconducting pairing (γσ) and a uniform on‑site potential (hσ). By imposing the symmetry t↑=−t↓, γ↑=−γ↓ and h↑=−h↓ the problem is reduced to a single set of parameters (t↑=1, γ≡γ↑, h≡h↑). The drive acts locally on the left boundary and simultaneously modulates the on‑site energy (cos ωt term) and an inter‑chain pairing (sin ωt term). In addition, each chain is coupled at both ends (sites j=1 and j=L) to Markovian baths that provide gain and loss with rates Γj,σ,g and Γj,σ,l chosen to respect an SO(2) symmetry.

Because the Hamiltonian is quadratic and the Lindblad jump operators are linear, the dynamics preserve Gaussianity. The full state is therefore encoded in the two‑point correlation matrix Cσ,σ′jk(t)=⟨c†j,σ ck,σ′⟩t. By moving to a rotating frame the explicit time dependence of the Hamiltonian is removed, yielding a time‑independent effective Lindbladian. The authors then apply the third‑quantization formalism to solve exactly for the non‑equilibrium steady state (NESS) of this effective Lindbladian. The laboratory‑frame, time‑averaged correlations are reconstructed from the rotating‑frame steady‑state correlations using simple linear relations (Eqs. 8‑9).

The central finding is that, even when the bulk of the static system lies deep in the trivial, gapped phase of the Kitaev chain (h>hc=1−γ², where correlations decay exponentially), the boundary drive can induce a non‑equilibrium phase transition to a state with long‑range correlations. The authors quantify long‑range order by the residual correlator \