Boundary-Driven Fermionic Chain Achieves Long-Range Correlations Despite Gapped Bulk States

Researchers have uncovered a surprising mechanism for creating long-range quantum correlations within a seemingly simple, yet fundamentally important, system: a chain of interacting fermions experiencing dissipation at its boundaries. Hao Chen, Wucheng Zhang, and Manas Kulkarni, from their respective institutions, alongside Abhinav Prem et al., demonstrate that a carefully tuned, periodic drive applied locally at the chain’s edges can induce this order, even when the bulk material exhibits no such behaviour. This non-equilibrium phase transition, driven by a resonance between the drive frequency and the bulk energy gaps, allows particles to propagate and establish correlations throughout the system. The findings are significant because they reveal a novel pathway for generating macroscopic quantum order in open systems, potentially offering new avenues for manipulating and controlling quantum information.

These chains are coupled via a coherent monochromatic drive acting locally on their first sites, described by a time-dependent Hamiltonian. Each chain is also connected to Markovian baths at its boundaries, introducing dissipation with specific gain and loss rates. The researchers analytically and numerically investigated the resulting non-equilibrium steady state, focusing on the correlation matrix to characterize the emergence of long-range order.

This approach allows for a detailed understanding of how the boundary drive influences the bulk properties of the system. This scaling relationship provides a quantitative measure of the strength of the induced order as a function of the system’s parameters. The study unveils a pathway for coherently controlling macroscopic order via precisely engineered local boundary couplings, a concept moving from theoretical abstraction towards experimental viability. This breakthrough reveals that a boundary-localized Floquet drive can stabilize macroscopic order deep within the bulk, even in systems where the static bulk is initially featureless. The research establishes a connection between boundary-driven phase transitions and the Floquet domain, offering a novel approach to coherent control in locally driven-dissipative quantum systems. This extends the understanding of how localized coherent driving can generate macroscopic order, potentially leading to new applications in quantum technologies.

Boundary Floquet Drive Induces Long-Range Fermionic Correlations

The study pioneered a method employing a Floquet drive, a time-periodic modulation, applied specifically to the boundaries of the fermionic chain, alongside boundary dissipation. The team engineered a precise control over the drive frequency to bridge energy gaps within the bulk, effectively creating pathways for boundary-injected excitations. This innovative approach enables the observation of correlations extending far beyond the immediate vicinity of the boundaries, a phenomenon not typically found in isolated, gapped systems. The research harnessed the power of this resonance mechanism to generate macroscopic order in an open system, challenging conventional understanding of correlation dynamics.

To quantify these correlations, scientists calculated the correlation matrix, a key observable that maps the relationships between different points in the fermionic chain. This method achieves a high degree of precision in characterizing the non-equilibrium steady state of the driven-dissipative system. Furthermore, the study employed advanced numerical techniques to simulate the behaviour of the fermionic chain under the influence of the Floquet drive and boundary dissipation. This computational work was crucial in validating the theoretical predictions and demonstrating the robustness of the observed phenomenon. The approach connects the innovative methodology, localized coherent driving, directly to the breakthrough finding of generating long-range order in open systems, highlighting its potential for applications in quantum information and materials science.

Floquet drive induces long-range fermionic correlations in strongly

Measurements confirm that the resonance mechanism allows for the propagation of excitations, effectively “opening” channels for correlation propagation. Researchers considered a system of two fermionic chains, each with parameters defining hopping amplitude (tσ), superconducting pairing potential (γσ), and on-site energy (hσ). The static Hamiltonian governing each chain yields a bulk energy spectrum defined by Ek,σ = ±2q(hσ + tσ cos k)² + γ²σ sin² k, where k represents the wavevector. The study employed a driving term, HD(t), acting locally on the first sites of the chains, modulating both the on-site energy and an inter-chain pairing term with a frequency ω.

Tests prove that this driving mechanism facilitates the correlated injection of single fermions into each chain. Data shows the system interacts with the environment through Markovian dissipation localized at the boundary sites, described by a Lindblad master equation governing the time evolution of the density matrix. The dissipation rates were set as Γ1,↑,g = 0.3, Γ1,↑,l = 0.5, ΓL,↑,g = 0.1, and ΓL,↑,l, ensuring symmetry in the dissipative dynamics. The breakthrough delivers a new pathway for coherent control in locally driven-dissipative quantum systems, extending the study of boundary-driven phase transitions into the Floquet domain.

Boundary Drive Induces Long-Range Fermionic Correlations in one

This scaling, confirmed through numerical analysis, demonstrates a quadratic dependence of the long-range correlation index on the pairing potential, highlighting the crucial role of particle-hole mixing in facilitating the propagation of excitations from the boundary into the bulk. These findings underscore the potential for manipulating macroscopic properties in open systems through localized, coherent driving, without requiring global parameter changes. The authors acknowledge that the limit of zero dissipation decouples the Hamiltonian into free fermion bands, preventing effective resonance between the drive and the bulk without the mediating pairing term. Furthermore, they note that establishing the critical nature of certain drive frequencies requires further investigation. Future research could explore the robustness of these findings in more complex systems and investigate the potential for utilizing this boundary control mechanism to engineer specific quantum states or functionalities.