Dissipative Kondo physics in the Anderson Impurity Model with two-body losses

Technical Summary: Dissipative Kondo Physics in the Anderson Impurity Model with Two-Body Losses

Problem Statement
The authors investigate the dynamics and steady-state properties of a dissipative Anderson Impurity Model (AIM) where a spinful electronic level is coupled to a metallic fermionic bath and subjected to Markovian two-body losses. While the standard AIM is a paradigmatic model for the Kondo effect, its dissipative extensions have recently attracted interest due to advances in quantum simulation with ultracold atoms and superconducting circuits. Specifically, the paper addresses the interplay between strong Coulomb repulsion ($U$) and correlated dissipation (two-body losses characterized by rate $\gamma$). The central question is whether Kondo physics, typically associated with coherent many-body screening, can survive or be modified by such incoherent particle loss processes, particularly in contrast to single-particle losses which are known to destroy many-body correlations.

Methodology
The study employs two primary theoretical approaches:

1. Non-Crossing Approximation (NCA) Dynamical Maps: The authors solve the many-body Lindblad master equation using a self-consistent hybridization expansion based on the NCA. This involves reformulating the Lindblad dynamics in a superfermion (purification) representation, where the density matrix is treated as a pure state in an extended Hilbert space. The method sums non-crossing diagrams to obtain a self-consistent equation for the dressed impurity time-evolution operator, allowing for the calculation of real-time dynamics, steady-state properties, and spectral functions in the thermodynamic limit.
2. Exact Quantum Trajectory Simulations: To benchmark the NCA results, the authors perform exact numerical simulations on finite-size chains (periodic boundary conditions) using the quantum jump method. This unravels the Lindblad dynamics into stochastic Schrödinger equations, averaging over trajectories to recover the density matrix evolution.
3. Dissipative Schrieffer-Wolff Transformation: To provide a physical interpretation of the results, the authors derive an effective low-energy model by applying a generalized Schrieffer-Wolff transformation to the Lindbladian. This integrates out the bath degrees of freedom to yield an effective Kondo model with residual impurity-bath losses.

Key Results

• Charge Dynamics and the Zeno Effect:
  The impurity charge density exhibits a non-monotonic dependence on the loss rate $\gamma$, a signature of the Quantum Zeno effect. For weak interactions ($U=0$), losses efficiently deplete the impurity. However, for strong interactions ($U \gg \Gamma$), the creation of doublons (doubly occupied states) is energetically blocked. Since two-body losses act only on doublons, strong correlations suppress the loss channel, causing the impurity to remain close to half-filling even at high dissipation rates. The loss current peaks at $\gamma \sim U$ and decreases at larger $\gamma$ as the system enters the Zeno regime where doublons are projected out.

• Spin Relaxation and Kondo-Zeno Crossover:
  The spin relaxation rate ($\tau_K^{-1}$) displays a characteristic non-monotonic behavior as a function of $\gamma$.

  • At weak dissipation, strong Coulomb repulsion suppresses spin relaxation, preserving the Kondo effect.
  • As $\gamma$ increases, dissipation initially aids spin decay by facilitating the formation and subsequent loss of doublons (a process that flips the spin).
  • At strong dissipation ($\gamma \gg U$), the system enters a Kondo-Zeno regime where the formation of doublons is suppressed by the Zeno effect, thereby closing the decay channel. Consequently, the spin relaxation rate decreases again, indicating a resurgence of Kondo physics.
    This non-monotonic behavior contrasts sharply with single-particle losses, which monotonically destroy spin correlations.

• Spectral Function Evolution:
  The impurity spectral function $A_\sigma(\omega)$ reveals distinct regimes:

  • Weak Losses: The upper Hubbard band (doublon band) is rapidly destroyed by dissipation, while the lower Hubbard band remains. The coherent Kondo peak at zero frequency is not immediately washed out but acquires a strongly asymmetric line shape; it is partially filled for negative frequencies while remaining sharply defined for positive ones.
  • Intermediate Losses: The Kondo peak collapses and merges with the lower Hubbard band, resulting in an incoherent featureless spectrum.
  • Strong Losses (Kondo-Zeno Regime): As doublons are completely projected out, a small coherent peak re-emerges at zero frequency, signaling a resurgence of Kondo correlations in the effective half-filled system.

• Comparison with Single-Particle Losses:
  The authors demonstrate that single-particle losses (modeled by jump operators $L \propto d_\sigma$) are far more destructive. They directly act on the single-particle sector, destroying both charge and spin excitations and washing out the Kondo peak even at moderate dissipation rates, without exhibiting a Zeno-protected regime.

• Effective Model:
  The Schrieffer-Wolff transformation yields an effective Kondo model with a renormalized coupling $J$ and residual non-local two-body losses. Crucially, the effective Kondo coupling $J$ remains finite even for $\gamma \gg U$, unlike in charge dephasing models where it vanishes. Furthermore, the residual dissipation strength $\kappa_{eff}$ is suppressed by either strong interactions ($U \gg \gamma$) or strong dissipation ($\gamma \gg U$), explaining the robustness of Kondo physics in both limits.

Significance and Claims
The paper claims to demonstrate that the interplay between strong Coulomb repulsion and correlated (two-body) dissipation gives rise to robust signatures of Kondo physics in both weak and strong dissipation limits. The key finding is that two-body dissipation, unlike single-particle dissipation, can protect Kondo physics. This protection arises because the dissipation mechanism (acting on doublons) is naturally suppressed by the strong correlations that define the Kondo state, and further suppressed by the Zeno effect at high loss rates.

The authors interpret the non-monotonic behavior of the spin relaxation rate and the re-emergence of the Kondo peak in the spectral function as evidence of a "Kondo-Zeno crossover." They conclude that the correlated nature of the dissipation is essential for retaining non-trivial many-body features, whereas uncorrelated (single-particle) losses destroy them. The results are supported by both NCA calculations in the thermodynamic limit and exact simulations on finite chains, with the latter confirming the qualitative features of the crossover. The work provides a theoretical framework for understanding dissipative quantum impurities in the context of recent experimental capabilities in ultracold atoms and quantum devices.