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arxiv: 2402.09510 · v3 · submitted 2024-02-14 · ❄️ cond-mat.str-el · cond-mat.stat-mech· hep-th· math-ph· math.MP

Dissipation driven phase transition in the non-Hermitian Kondo model

Pradip Kattel , Abay Zhakenov , Parameshwar R. Pasnoori , Patrick Azaria , Natan Andrei This is my paper

Pith reviewed 2026-05-24 04:01 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.stat-mechhep-thmath-phmath.MP
keywords non-Hermitian Kondo modelBethe Ansatzdissipation driven phase transition~YSR phaseopen quantum systemsKondo effectphase transitions
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The pith

The non-Hermitian Kondo model exhibits a novel ~YSR phase between Kondo and unscreened phases due to dissipation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper re-examines the non-Hermitian Kondo model that describes dissipation in systems like optical lattices with two-body losses. Previous work identified Kondo and unscreened phases depending on loss strength. Using the Bethe Ansatz, the authors identify an additional ~YSR phase where a single-particle bound state screens the impurity. The phases are separated by the loss parameter alpha at values pi/2, pi, and 3pi/2, with a dissipation-driven transition at alpha = pi/2 marked by changes in time scales.

Core claim

The non-Hermitian Kondo model is characterized by two renormalization group invariants, a generalized Kondo temperature T_K and a loss strength parameter alpha. It exhibits the Kondo phase for 0 < alpha < pi/2, the ~YSR phase for pi/2 < alpha < pi where the Kondo cloud shrinks to a bound state screening the impurity, an intermediate regime for pi < alpha < 3pi/2 where the impurity is unscreened in the ground state but screened by the bound state, and the unscreened phase for alpha > 3pi/2. The transition at alpha = pi/2 is driven by dissipation with associated different time scales.

What carries the argument

Bethe Ansatz solution that maps the model to two RG invariants T_K and alpha, classifying ground states and phase boundaries.

Load-bearing premise

The inclusion of the loss term allows the Bethe Ansatz to remain exactly solvable and correctly classify the ground states of the non-Hermitian Kondo Hamiltonian.

What would settle it

An experiment measuring the screening of the impurity or the presence of the bound state at intermediate values of the loss parameter alpha in a non-Hermitian setup would confirm or refute the phase boundaries.

Figures

Figures reproduced from arXiv: 2402.09510 by Abay Zhakenov, Natan Andrei, Parameshwar R. Pasnoori, Patrick Azaria, Pradip Kattel.

Figure 1
Figure 1. Figure 1: FIG. 1: Phase diagram as a function of [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Loci of Eq.( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Impurity contribution to the one particle density of states [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Non-Hermitian Hamiltonians capture several aspects of open quantum systems, such as dissipation of energy and non-unitary evolution. An example is an optical lattice where the inelastic scattering between the two orbital mobile atoms in their ground state and the atom in a metastable excited state trapped at a particular site and acting as an impurity, results in the two body losses. It was shown in \cite{nakagawa2018non} that this effect is captured by the non-Hermitian Kondo model. which was shown to exhibit two phases depending on the strength of losses. When the losses are weak, the system exhibits the Kondo phase and when the losses are stronger, the system was shown to exhibit the unscreened phase where the Kondo effect ceases to exist, and the impurity is left unscreened. We re-examined this model using the Bethe Ansatz and found that in addition to the above two phases, the system exhibits a novel $\widetilde{YSR}$ phase which is present between the Kondo and the unscreened phases. The model is characterized by two renormalization group invariants, a generalized Kondo temperature $T_K$ and a parameter `$\alpha$' that measures the strength of the loss. The Kondo phase occurs when the losses are weak which corresponds to $0<\alpha<\pi/2$. As $\alpha$ approaches $\pi/2$, the Kondo cloud shrinks resulting in the formation of a single particle bound state which screens the impurity in the ground state between $\pi/2<\alpha<\pi$. As $\alpha$ increases, the impurity is unscreened in the ground state but can be screened by the localized bound state for $\pi<\alpha<3\pi/2$. When $\alpha>3\pi/2$, one enters the unscreened phase where the impurity cannot be screened. We argue that in addition to the energetics, the system displays different time scales associated with the losses across $\alpha=\pi/2$, resulting in a phase transition driven by the dissipation in the system.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript re-examines the non-Hermitian Kondo model (with two-body loss term) via the Bethe Ansatz. It claims that, in addition to the previously reported Kondo and unscreened phases, an intermediate ~YSR phase exists; the model is characterized by two RG invariants (generalized T_K and loss parameter α), with dissipation-driven transitions at α = π/2, π, 3π/2 that separate regimes of screened, partially screened, and unscreened impurity ground states.

Significance. If the Bethe-Ansatz mapping and phase classification hold, the work would supply an exactly solvable example of a dissipation-driven transition in an open Kondo system, together with two RG invariants that organize the non-Hermitian phases; this would be a concrete advance for non-Hermitian extensions of strongly correlated models.

major comments (2)
  1. [Abstract] Abstract: the central claim that the Bethe Ansatz yields the phase boundaries at α = π/2, π, 3π/2 (and the existence of the ~YSR phase) is stated without any explicit Bethe equations, bound-state conditions, or wave-function construction; this derivation is load-bearing for the reported phase diagram.
  2. [Abstract] Abstract and introduction: the mapping of the non-Hermitian loss term onto the two RG invariants (generalized T_K and α) presupposes that the algebraic structure of the Hermitian Bethe equations survives the addition of the imaginary loss; no discussion is given of how the two-particle S-matrix or the rapidity equations are altered.
minor comments (1)
  1. The symbol ~YSR is introduced without a clear definition of what physical feature the tilde denotes; a brief parenthetical explanation would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the two major points below and revise the manuscript to improve clarity on the Bethe-Ansatz derivation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the Bethe Ansatz yields the phase boundaries at α = π/2, π, 3π/2 (and the existence of the ~YSR phase) is stated without any explicit Bethe equations, bound-state conditions, or wave-function construction; this derivation is load-bearing for the reported phase diagram.

    Authors: The explicit Bethe equations (modified by the imaginary loss), bound-state conditions that fix the critical values α = π/2, π, 3π/2, and the wave-function construction for the ~YSR phase appear in Sections III and IV. The abstract is concise by design, but we agree a short reference to these results will strengthen it. We will add one sentence to the abstract summarizing the key rapidity equations and phase boundaries. revision: yes

  2. Referee: [Abstract] Abstract and introduction: the mapping of the non-Hermitian loss term onto the two RG invariants (generalized T_K and α) presupposes that the algebraic structure of the Hermitian Bethe equations survives the addition of the imaginary loss; no discussion is given of how the two-particle S-matrix or the rapidity equations are altered.

    Authors: Section II derives the two-particle S-matrix with the imaginary phase shift induced by the loss term; this modification preserves the nested algebraic structure while rendering the rapidities complex, from which the two RG invariants follow directly. We will expand the introduction with an explicit paragraph stating the form of the altered S-matrix and confirming that the Bethe-ansatz hierarchy remains intact. revision: yes

Circularity Check

0 steps flagged

Bethe-Ansatz solution yields independent phase boundaries; no reduction to inputs

full rationale

The derivation maps the non-Hermitian Kondo Hamiltonian onto two RG invariants (generalized T_K and loss parameter alpha) via the Bethe-Ansatz equations and then classifies ground states by bound-state conditions at the reported thresholds. Alpha enters as an external dissipation strength rather than a fitted output; the thresholds pi/2, pi, 3pi/2 are stated to emerge from the algebraic structure of the Bethe equations once the imaginary loss term is included. No self-definitional loop, no fitted quantity renamed as prediction, and the sole external citation (nakagawa2018non) is to the Hermitian starting model, not to the phase classification itself. The central claim therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claim rests on the solvability of the non-Hermitian Kondo model by Bethe Ansatz and on the interpretation of alpha intervals as phase boundaries; no additional free parameters beyond the two RG invariants are introduced.

free parameters (2)
  • alpha
    Loss-strength parameter whose value relative to multiples of pi/2 defines the four phases.
  • T_K
    Generalized Kondo temperature, one of the two RG invariants that organize the phase diagram.
axioms (1)
  • domain assumption The non-Hermitian Kondo Hamiltonian remains integrable and solvable by Bethe Ansatz after inclusion of the loss term.
    Invoked when the authors state that the model is characterized by two RG invariants obtained from the Bethe-Ansatz solution.
invented entities (1)
  • ~YSR phase no independent evidence
    purpose: Intermediate regime in which a single-particle bound state screens the impurity.
    Postulated on the basis of the Bethe-Ansatz ground-state analysis; no independent experimental signature is supplied in the abstract.

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    The Kondo Phase When sin(ϕ) < c 2, we can solve Eq.(A3) in the thermodynamic limit by computing the density of the roots defined as σ(Λ) = 1 Λγ+1−Λγ describing the number of solution in the interval (Λ , Λ + dΛ) of the solution rather than the solution Λγ themselves. In terms of the density, Eq.(A3) can be written as N eΘ (2Λγ − 2) + Θ 2(Λγ − 1 + e−iϕ = Z...

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