Kondo breakdown as an entanglement transition driven by continuous measurement

Abstract

We study the breakdown of Kondo screening by a local magnetic field from the perspective of a measurement-driven entanglement transition in a monitored quantum system. Here, the Kondo coupling leads to the growth in entanglement of an impurity spin with it's fermionic environment, while the local field plays the role of a continuous observer. Using a non-perturbative Unitary Renormalization Group (URG) approach, we derive coupled renormalization-group flow equations for the Kondo exchange and the local field, and obtain a field-dependent RG phase diagram. The RG flows separate a low-energy Kondo-screened phase, where the impurity is absorbed into the Fermi sea and forms an entangled singlet with the conduction bath, from a polarized local-moment phase in which screening is frustrated and impurity-bath entanglement is suppressed. We identify the fixed-point Hamiltonians governing the two phases and the critical regime, and relate the transition to the emergence of a novel non-Fermi liquid. Various impurity signatures such as the spectral function and thermalisation of impurity observables are used to characterise this entanglement transition. These results offer insight into the interplay of decoherence and measurement in governing the dynamics of a prototypical quantum system.

Figures (19)

• Figure 1: Schematic diagram illustrating a single step of the URG process. One application of the unitary RG transformation decouples the fermionic states $n_j$ and modifies the couplings for the remaining states into new Hamiltonians $\tilde{H}_1$ and $\tilde{H}_0$.
• Figure 2: Schematic RG phase diagram representing a measurement-induced quantum phase transition between the Kondo screened (top left) and local moment (bottom right) fixed points of the Kondo problem in a local B-field.
• Figure 3: RG flows showing relevant $J$ and irrelevant $B$ for a small external magnetic field in the Kondo screened regime.
• Figure 4: RG flows showing irrelevant $J$ and relevant $B$ for the local moment regime.
• Figure 5: Schematic diagram of the quantum-to-classical phase transition: the magnetic field induces a transition from the quantum singlet state to the classical localized state, where $g=\frac{\mu_B B}{J}$.