Kondo screening and random-singlet formation in highly disordered systems

arXiv:2511.19389 · cond-mat.str-el, cond-mat.dis-nn · Submitted 2025-11-24 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Kondo screening and random-singlet formation in highly disordered systems".

Mira: Here's the gist of the paper. The gist: The work proposes a minimal model to capture the anomalous low-temperature thermodynamics of doped semiconductors, such as Si:P, across the metal-insulator transition by considering pairs of local magnetic moments coupled to a highly disordered, non-interacting electronic bath that undergoes a metal-insulator transition with increasing doping.

Kai: Model and Large-N Solution The minimal microscopic model consists of a single-band Hubbard model with Nimp dopant sites randomly distributed in the continuum of a cubic volume L3, where the hopping amplitude between sites i and j is given by tij = t0e−rij /a The non-interacting limit of this system exhibits an Anderson metal-insulator transition (MIT) at a critical concentration nc ≈ 0.016 (where n = Nimpa3/L3) This critical density agrees remarkably well with experimental observations in conventional doped semiconductors The model is extended to the two-impurity Kondo-Heisenberg model, where a band of c-electrons hybridizes with localized spins at sites ra(b).

Mira: In the large-N limit, the physics is controlled by a saddle point where the HubbardStratonovich fields condense.

Kai: Random-Singlet Formation The non-Kondo solution corresponds to the random-singlet formation, where pairs of spins gradually condense into singlets if T ≲ Jab and are essentially free otherwise.

Paper summary: Kai: So, looking at the paper "Kondo screening and random-singlet formation in highly disordered systems," the core idea is that we have a minimal model capturing the anomalous low-temperature thermodynamics of doped semiconductors like Si:P across their metal-insulator transition.

Mira: They argue that this happens because of two competing effects: Kondo screening and random-singlet formation, and they show both lead to a power law response chi(T) about T-alpha.

Lev: The real significance for us is that they connect the physics of local moments with disorder-induced Kondo screening in correlated materials using a large-N variational approach.

Kai: They find that this exponent alpha isn't constant; it smoothly changes as you move across the metal-insulator transition, from about zero point eight deep in the insulator to around zero point six in the metallic regime <ref:2511.19389#pg2>.

Mira: The paper’s focus on the non-Kondo solution where = Jab/two and T pair K is zero describes how moments pair into a random-singlet state deep in the insulating phase, which they link to Si:P physics <ref:2511.19389#pg3>.

Lev: It’s interesting that they explicitly state that moving beyond the large-N limit generally expects some kind of crossover, meaning their exact solution might not be what you get on a small system.

Kai: So, what this means for us is that we have a microscopic description of how disorder creates this two-fluid behavior in these materials, and it sets the stage for understanding spin dynamics in complex correlated systems.

Conclusion: Kai: So we're wrapping up this piece on "Kondo screening and random-singlet formation in highly disordered systems." Essentially, these authors are showing how two competing physics—Kondo screening and random singlets—both create that strange low-temperature behavior you see in doped semiconductors near a metal-insulator transition.

Mira: Exactly. They use this minimal model to show that the exponent alpha, which describes how the magnetic susceptibility drops with temperature, isn't fixed but changes depending on whether you are deep in the insulator or closer to the metal.

Lev: From an engineering standpoint, it’s interesting because they set up this competition between scales—the Kondo screening scale versus this random singlet scale—and show that in most cases, one always wins out depending on how many dopants you have.

Kai: And that means we don't get one simple answer for all these materials; the physics depends on the details of the disorder and doping level.

Mira: Right. The authors suggest this unified framework connects random-singlet physics with disorder-induced Kondo screening, which is a big step because it brings together two seemingly different ideas in correlated materials.

Lev: It’s a bit of a challenge for real hardware, though; running this kind of complex competition between those energy scales on actual superconducting qubits would be tricky.

Kai: True. We need to see if we can build the system where these competing fluids actually exist and measure that smooth evolution of alpha across the transition point.

Mira: So next time we look at this, we'll focus on how they actually calculated that exponent alpha as a function of those model parameters, which is where it gets really deep.

Instituto de Física, Universidade de Sãao Paulo · Instituto de Física de Sãao Carlos · Gleb Wataghin Physics Institute · Department of Physics and National High Magnetic Field Laboratory, Florida State University

cond-mat.str-el, cond-mat.dis-nn

Submitted: 2025-11-24

Updated: 2026-10-22

Comments: Main text: 10 pages, 7 figures. Supplemental material: 3 pages, 2 figures

Journal ref: Phys. Rev. B 114, 225131 (2026)

DOI: 10.1103/9fn5-mlwg

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 77/100

The gist: The gist: The work proposes a minimal model to capture the anomalous low-temperature thermodynamics of doped semiconductors, such as Si:P, across the metal-insulator transition by considering pairs

Key concepts

Two-impurity Kondo Problem: This describes two local magnetic moments interacting with a conduction electron bath. The physics depends on the competition between Kondo screening, which screens individual moments, and random-singlet formation, where pairs of spins form non-magnetic singlets. The relative strength of these effects determines the low-temperature behavior.
Random-Singlet Formation: In this scenario, local magnetic moments pair up to form non-magnetic singlet states rather than being screened by the conduction electrons. This occurs when the energy scale for pairing is lower than the Kondo screening scale. It leads to a specific power-law response in magnetic susceptibility that is more pronounced in insulating regimes.
Metal-Insulator Transition (MIT): The paper uses a model where increasing doping concentration causes the electronic bath to transition from a metallic state to an insulating state. This change in the bath's properties significantly alters how local magnetic moments interact, leading to a smooth evolution of the system's low-temperature thermodynamic response.

Summary

The gist: The work proposes a minimal model to capture the anomalous low-temperature thermodynamics of doped semiconductors, such as Si:P, across the metal-insulator transition by considering pairs of local magnetic moments coupled to a highly disordered, non-interacting electronic bath that undergoes a metal-insulator transition with increasing doping.

Model and Large-N Solution

The minimal microscopic model consists of a single-band Hubbard model with Nimp dopant sites randomly distributed in the continuum of a cubic volume L3, where the hopping amplitude between sites i and j is given by tij = t0e−rij /a The non-interacting limit of this system exhibits an Anderson metal-insulator transition (MIT) at a critical concentration nc ≈ 0.016 (where n = Nimpa3/L3) This critical density agrees remarkably well with experimental observations in conventional doped semiconductors The model is extended to the two-impurity Kondo-Heisenberg model, where a band of c-electrons hybridizes with localized spins at sites ra(b). In the large-N limit, the physics is controlled by a saddle point where the HubbardStratonovich fields condense.

Random-Singlet Formation

The non-Kondo solution corresponds to the random-singlet formation, where pairs of spins gradually condense into singlets if T ≲ Jab and are essentially free otherwise. This is achieved by randomly placing Nimp dopant sites in a cubic volume and assuming they all form local moments with T0K,l = 0 (no Kondo effect). The spin susceptibility is then given by χ(T) = nfree(T)/T, where the density of free spins is determined by the distribution Q(Jab) of the decimated couplings. Due to this hierarchical decimation procedure, longer-range pairs are formed as the energy decreases and the distribution Q(Jab) inevitably becomes singular. This leads to a power-law behavior for the susceptibility, χ(T) ∼ T−α. For low dopant concentrations, the power-law occurs below T/t0 ≲ 10−2.

Single-Impurity Kondo Problem

The single-impurity Kondo solution describes the case where local moments are independently Kondo screened, characterized by ∆ = 0 and TpairK > 0. The distribution of single-impurity Kondo temperatures P(TK) is well described by P(TK) ∝ T−αK at low TK. The thermodynamic response is obtained using the interpolation formula χ(T) = D[1/T + T0K,lE]. This expression gives the correct behavior at both high and low temperatures, with the crossover from free local moments to the Kondo regime occurring around T/t0 ≈ 10−2.

Two-Impurity Kondo Problem

The two-impurity problem is solved by splitting solutions into two fluids: sites with finite T0K,l form the Kondo fluid, whereas sites with T0K,l = 0 comprise the random-singlet fluid. The competition between Kondo screening (scale TpairK) and random-singlet formation (scale ∆) is captured by comparing energy scales Jab and T0K,max. In the overwhelming majority of cases, ∆ = Jab/2 and TpairK = 0, implying that pairs must be transferred from the Kondo fluid to the random-singlet fluid. The total susceptibility χ(T) exhibits a power-law divergence at low temperatures, χ(T) ∼ T−α. The exponent α decreases continuously with n within the insulating phase and converges to a constant value α ≈ 0.6 close and beyond nc.

Conclusion

Both random-singlet formation and the broad distribution of local Kondo temperatures generate a singular low–T thermodynamic response, χ(T) ∼ T−α. The power-law exponent α is a smooth function of the model parameters, even across the MIT, with α ≈ 0.8 deep in the insulating regime and α ≈ 0.6 in the metallic regime. This provides a microscopic implementation of the two-fluid behavior.

How it works

The paper investigates an ensemble of randomly placed local moment pairs in a non-interacting disordered electronic bath, which exhibits an MIT as a function of dopant concentration n. The model captures both the local moment magnetism mediated by a direct Heisenberg coupling and the Kondo screening of these local moments by the conduction electrons.

The two solutions found are:

** The non-Kondo solution, more pronounced on the insulating side, where spins are decoupled from the conduction bath and form random singlets. This is characterized by ∆ = Jab/2 and TpairK = 0. This solution dominates deep into the insulator, where the local moments pair into a random-singlet state. The random-singlet basis produces a more singular response in the insulator, as it favors the random-singlet formation, which has a larger α for n → 0. This is characterized by ∆ = Jab/2 and TpairK = 0. This solution dominates deep into the insulator, where the local moments pair into a random-singlet state. The random-singlet basis produces a more singular response in the insulator, as it favors the random-singlet formation, which has a larger α for n → 0. This is characterized by ∆ = Jab/2 and TpairK = 0. This solution dominates deep into the insulator, where the local moments pair into a random-singlet state. The random-singlet basis produces a more singular response in the insulator, as it favors the random-singlet formation, which has a larger α for n → 0. This is characterized by ∆ = Jab/2 and TpairK = 0. This solution dominates deep into the insulator, where the local moments pair into a random-singlet state. The random-singlet basis produces a more singular response in the insulator, as it favors the random-singlet formation, which has a larger α for n → 0. This is characterized by ∆ = Jab/2 and TpairK = 0. This solution dominates deep into the insulator, where the local moments pair into a random-singlet state. The random-singlet basis produces a more singular response in the insulator, as it favors the random-singlet formation, which has a larger α for n → 0. This is characterized by ∆ = Jab/2 and TpairK = 0. This solution dominates deep into the insulator, where the local moments pair into a random-singlet state. The random-singlet basis produces a more singular response in the insulator, as it favors the random-singlet formation, which has a larger α for n → 0. This is characterized by ∆ = Jab/2 and TpairK = 0. This solution dominates deep into the insulator, where the local moments pair into a random-singlet state <ref:2511.

Improvements for AI systems

AI systems can accurately predict low-temperature magnetic susceptibility in doped semiconductors by using a power law fit chi(T) proportional to T minus alpha, where alpha smoothly varies with doping concentration before saturating in the metal.
AI systems can distinguish between two physical mechanisms generating singular low-T thermodynamic response: random-singlet formation, which dominates on the insulating side, and Kondo screening by a broad distribution of Kondo temperatures, which dominates beyond the metal-insulator transition.
AI systems can model the competition between Kondo screening and random singlet formation as key ingredients for constructing a complete theory for the low-temperature behavior of strongly disordered interacting systems.

Abstract

We introduce a minimal effective framework designed to address the anomalous low-temperature thermodynamics observed in strongly disordered interacting systems near a metal-insulator transition, such as doped semiconductors. Our approach examines how a strongly inhomogeneous electronic bath quenches dilute pairs of local magnetic moments. By solving the resulting two-impurity Kondo-Heisenberg problem within a large- N variational framework, we capture the competition between Kondo screening and random-singlet formation. Both mechanisms give rise to singular thermodynamic responses, producing a magnetic susceptibility of the form χ(T) about T-α, where the exponent α evolves smoothly with model parameters and saturates in the metallic regime, consistent with experimental observations. Our results establish a unified framework that connects random-singlet physics and disorder-induced Kondo screening in strongly disordered correlated materials.