Pseudogap and Non-Fermi-liquid criticality in double Kondo model for bilayer nickelates

arXiv:2603.25742 · cond-mat.str-el · Submitted 2026-03-26 · 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: "Pseudogap and Non-Fermi-liquid criticality in double Kondo model for bilayer nickelates".

Mira: Here's the gist of the paper. The gist The investigation into bilayer nickelates using single-site dynamical mean-field theory (DMFT) reveals that a pseudogap metal phase, termed 'second Fermi liquid' (sFL), exists in the underdoped regime, separated from a conventional Fermi liquid (FL) by a non-Fermi-liquid (NFL) critical point tuned by interlayer spin coupling or hole doping<ref:2603.25742#pg2>.

Kai: Model and Methodology The study employs the double Kondo lattice model for bilayer nickelates, which describes each layer with itinerant electrons on the dx2−y2 orbital coupled to localized moments on the dz2 orbital via a ferromagnetic coupling JK = −2JH < 0, and these local moments are further coupled by an antiferromagnetic exchange J⊥ > 0<ref:2603.25742#pg2>.

Mira: This model is suitable for single-site DMFT calculations combined with a numerical renormalization group (NRG) impurity solver to access low-energy physics nonperturbatively<ref:2603.25742#pg2>.

Kai: The phase diagram is mapped as a function of J⊥, hole doping x, and the Hund’s coupling JK = −2JH<ref:2603.25742#pg2>.

Paper summary: Kai: So, we're looking at this paper today, "Pseudogap and Non-Fermi-liquid criticality in double Kondo model for bilayer nickelates." It’s motivated by some recent experimental work on high-temperature superconductivity in bilayer nickelates.

Mira: Exactly. The core idea here is using single-site dynamical mean-field theory, DMFT, to map out the normal state phase diagram of a bilayer Kondo lattice model. What they claim is that when you turn off the interlayer tunneling t perped, you find a non-Fermi liquid critical point tuned by either the interlayer spin coupling J perped or by hole doping x.

Lev: So what's this separating? What kind of phases are we talking about?

Kai: They separate a standard Fermi liquid in the overdoped region from a distinct pseudogap metal in the underdoped regime. That pseudogap phase, which they call the second Fermi liquid, or sFL, has small hole pockets and it actually violates the perturbative Luttinger theorem even though there's no symmetry breaking or fractionalization happening.

Mira: A heavy Fermi liquid behaving like a standard one but with a small quasi-particle residue and a large effective mass. And they give us an intuitive analytical description of this pseudogap and the ground-state wave function using an ancilla fermion framework.

Lev: The method sounds computationally intensive because they're using single-site DMFT with a numerical renormalization group impurity solver to get the low-energy physics nonperturbatively. That means this is a strong result for the model, but what does that actually mean for real hardware?

Kai: Well, for me, it means we have a theoretical roadmap. They show how to find that NFL region where things get strange when you tune J perped or x. It tells us exactly what kind of physics to look for when we try to engineer these correlated electron systems in our superconducting qubits.

Mira: And the connection they draw is interesting because they extend this analysis to include finite interlayer hopping t perped and apply it specifically to the bilayer nickelate La3Ni2O7. They propose that current experimental samples, which have a doping x around zero point five, are actually sitting in the overdoped Fermi liquid regime <ref:2603.25742#pg3>.

Lev: If they’re in the FL regime at x equals zero point five, how does that change our expectations for what we might measure if we try to probe this strange metal behavior <ref:2603.25742#pg3>?

Kai: It suggests that the pseudogap phase and the non-Fermi liquid criticality might actually be accessible if we electron dope these materials further. So, doping seems like a pathway into that NFL physics.

Mira: The paper also provides some deep connections to other systems, suggesting that the strange metal behavior in bilayer nickelates could originate from this quantum critical point between the pseudogap metal and the Fermi liquid itself.

Lev: And they link this to twisted bilayer graphene, suggesting a similar sFL phase might control the normal state of that material too. That's a pretty broad connection for something so specific like this model study.

Kai: It’s interesting because they tie it all together by suggesting that the quantum critical point discussed here is related to the non-Fermi liquid QCP found in the two-impurity Anderson model. It puts this within a broader context of correlated electron physics.

Mira: And to summarize, the main thing we take away from "Pseudogap and Non-Fermi-liquid criticality in double Kondo model for bilayer nickelates" is that they've identified a second Fermi liquid phase, the sFL, separated from a conventional Fermi liquid by an NFL critical point tuned by J perped or x.

Lev: So, what's the bigger picture for us building error correction? Does this suggest any specific constraints on how we need to handle these correlated states in our physical systems?

Kai: It suggests that if we're working with a system that exhibits this kind of sFL behavior, we need to be very careful about how we define the quasiparticle weight Z, because it goes to zero at the critical point.

Mira: The whole thing hinges on the assumption that this model accurately captures the physics of bilayer nickelates, and they do that by using a specific double Kondo lattice model description where you have itinerant electrons on one orbital coupled to localized moments via a ferromagnetic coupling J perperped.

Lev: And what about the limitations? What does the paper admit it doesn't cover?

Kai: They don't fully map out how to implement this exactly on real hardware, but they do provide an intuitive framework using an ancilla fermion as a spin-polaron to model the pseudogap behavior.

Mira: That ancilla fermion concept is key because it helps visualize how the small hole pockets appear around that pi pi point in the wavefunction, which is crucial for understanding why it looks like a heavy Fermi liquid with suppressed spectral weight on the original band.

Lev: If we had to translate this into an actual error correction setup, I'd say we'd need to focus on controlling those small quasi-particle residues that they mention are reduced in the sFL phase.

Kai: Right, so while it doesn't give us a direct blueprint for the material science experiment yet, it gives us the theoretical language to describe what we hope to observe when we push doping into these systems. That’s what this paper is doing.

Conclusion: Kai: So we've looked at how they mapped out this weird phase diagram for bilayer nickelates using single-site DMFT, and now we're getting to the conclusion of "Pseudogap and Non-Fermi-liquid criticality in double Kondo model for bilayer nickelates."

Mira: Basically, they show that there’s a standard Fermi liquid on one side and this second Fermi liquid phase called the sFL on the other side, with a non-Fermi liquid critical point right in between them.

Lev: The authors used a model based on double Kondo lattices to get these results, and they found that this transition is tuned by things like the interlayer spin coupling J perped or by hole doping x.

Kai: What this means for the real world is that we can start looking for these non-Fermi liquid behaviors when we tune materials in different ways, specifically through doping or changing how those layers talk to each other.

Mira: It suggests that this strange metal behavior you see in some nickelates might be coming from exactly this critical point between the two distinct Fermi liquid states.

Lev: From an error correction standpoint, if the physics is indeed governed by a QCP like this, we need to be really careful about how we define the quasiparticle weight Z because it vanishes right at that point.

Kai: So while they've given us a solid model description for what’s happening in the underdoped regime, their next step is showing how this connects to other systems and whether electron doping can actually take us into that interesting sFL region.

Mira: They also mentioned links to twisted bilayer graphene and the two-impurity Anderson model, which suggests this type of critical behavior isn't just a fluke in nickelates.

Lev: If we want to build something based on this, we need to figure out how much overhead running those calculations would actually land on real hardware when you try to simulate that sFL state.

Kai: That's the next big question—how do we translate this theoretical picture into something that a physical quantum computer or experimental setup could even measure?

Department of Physics and Astronomy, Johns Hopkins University

cond-mat.str-el

Submitted: 2026-03-26

Updated: 2026-10-20

Comments: 34 pages, 23 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 74/100

The gist: The gist The investigation into bilayer nickelates using single-site dynamical mean-field theory (DMFT) reveals that a pseudogap metal phase, termed 'second Fermi liquid' (sFL), exists in the

Key concepts

Second Fermi Liquid (sFL): This is a distinct metallic phase found in the underdoped regime of bilayer nickelates. It differs from a standard Fermi liquid because it exhibits small hole pockets and violates the usual Luttinger theorem, behaving like a heavy Fermi liquid with a large effective mass.
Non-Fermi Liquid (NFL) Critical Point: This is a quantum critical point where the conventional metallic state transitions into the sFL phase. It is tuned by parameters like interlayer spin coupling or hole doping. In this critical region, standard Fermi liquid behavior breaks down, leading to anomalous transport properties.
Ancilla Fermion Framework: A theoretical tool used to describe the pseudogap phase. The ancilla fermion acts as a spin-polaron composite operator that hybridizes with the electron. This framework helps explain the emergent Kondo-like resonance peak observed in DMFT calculations within the sFL.
Pseudogap Behavior: This is a characteristic of the sFL phase where spectral weight is suppressed at positive energies, indicated by a divergent self-energy ($\Sigma(\omega) \sim \Phi^2/(\omega + \mu\psi)$). This suppression leads to a dip in the spectral function and suggests that most low-energy physics is dominated by the composite fermion.

Terminology

Symmetry Breaking — 1× in this paper · explained in 4 episodes

Summary

The gist The investigation into bilayer nickelates using single-site dynamical mean-field theory (DMFT) reveals that a pseudogap metal phase, termed 'second Fermi liquid' (sFL), exists in the underdoped regime, separated from a conventional Fermi liquid (FL) by a non-Fermi-liquid (NFL) critical point tuned by interlayer spin coupling or hole doping<ref:2603.25742#pg2>.

Model and Methodology

The study employs the double Kondo lattice model for bilayer nickelates, which describes each layer with itinerant electrons on the dx2−y2 orbital coupled to localized moments on the dz2 orbital via a ferromagnetic coupling JK = −2JH < 0, and these local moments are further coupled by an antiferromagnetic exchange J⊥ > 0<ref:2603.25742#pg2>. This model is suitable for single-site DMFT calculations combined with a numerical renormalization group (NRG) impurity solver to access low-energy physics nonperturbatively<ref:2603.25742#pg2>. The phase diagram is mapped as a function of J⊥, hole doping x, and the Hund’s coupling JK = −2JH<ref:2603.25742#pg2>.

Phase Diagram and Criticality

The DMFT+NRG calculations identify two distinct Fermi liquid phases: a conventional FL in the overdoped region with a large Fermi surface area AFL = (1 − x)/2, and a second Fermi liquid (sFL) in the underdoped regime with a small Fermi surface area AsFL = −x/2<ref:2603.25742#pg2>. The transition between these phases is continuous and occurs at a quantum critical point (QCP) where the quasiparticle weight Z vanishes, accompanied by a jump in the Fermi surface volume per flavor of ∆AFS ≃ ±1/2<ref:2603.25742#pg2>. In the critical regime, NFL behaviors are observed, including log divergence of susceptibility for bosonic operators such as the total density and layer-alternating spin<ref:2603.25742#pg2>.

Pseudogap Characteristics

The pseudogap behavior in the sFL phase is manifested as a divergent structure in the self-energy, approximated by Σ(ω) ∼ Φ 2/(ω + µψ)<ref:2603.25742#pg2>. This leads to a dip in the spectral function Ac(ω) at positive energy, and an emergent composite fermion dominates at low energy, confirmed by a Kondo-like resonance peak in the spectral function of this composite fermion<ref:2603.25742#pg2>. The ancilla framework provides a model wavefunction where the pseudogap arises from hybridization between the electron and the ancilla fermion, leading to a small hole-like Fermi pocket around (π, π)<ref:2603.25742#pg2>.

Role of Interlayer Coupling

The interlayer spin coupling J⊥ plays a crucial role in stabilizing the sFL phase; for strong ferromagnetic Hund’s coupling (JH ≳ 2.5t), the sFL is stabilized by stronger J⊥ and smaller doping x, with the critical doping xc increasing with increasing J⊥<ref:2603.25742#pg2>. Conversely, for anti-Hund’s coupling (JK > 0), a larger J⊥ favors the FL (RKKY-like) phase, suggesting that interlayer singlet formation competes with Kondo hybridization<ref:2603.25742#pg2>. Finite interlayer hopping t⊥ breaks the separate U(1)t × U(1)b symmetry down to a single global U(1) symmetry, which is important for understanding the stability of NFL behavior near the QCP<ref:2603.25742#pg2>.

Connection to Other Systems

The results suggest that the strange-metal behavior observed in bilayer nickelates may originate from this QCP between the pseudogap metal and the Fermi liquid<ref:2603.25742#pg2>. Furthermore, a deep connection is suggested between bilayer nickelates and twisted bilayer graphene (TBG), as a similar sFL phase may control the normal state of TBG<ref:2603.25742#pg2>. The quantum critical point discussed is closely related to the non-Fermi liquid QCP of the two-impurity Anderson model (2IAM)<ref:2603.25742#pg2>.

Ancilla Fermion Interpretation

The ancilla fermion can be interpreted as a spin-polaron like trion operator, which is identified through an equation-of-motion hierarchy of the electron Green’s function<ref:2603.25742#pg2>. This composite operator carries the same charge, spin and fermionic statistics as the original electron operator<ref:2603.25742#pg2>. A variational wave function can be constructed by projecting the ancilla wave function onto the physical Hilbert space, which is expected to capture the correct low-energy physics<ref:2603.25742#pg2>.

Fermi Surface Evolution

While direct experimental detection of small Fermi pockets is difficult, their presence is inferred from transport measurements<ref:2603.25742#pg2>. In the sFL phase, the spectral weight on the original dispersive band is strongly suppressed in −1/πIm Iα(ω), and most of it is transferred to a nearly flat band at low energy, corresponding to the contribution from ΨJi;α together with a broad high-energy feature associated with ΨUi;α<ref:2603.25742#pg2>. The evolution of the small Fermi surface gradually broadens into a large Fermi-surface-like structure at energies of order ∼ 10−2t<ref:2603.25742#pg2>.

Conclusion

The study successfully identifies both a conventional FL in the overdoped region and a pseudogap metal sFL in the underdoped regime, separated by an NFL critical region<ref:2603.25742#pg2>. The findings suggest that future experiments should search for the PG phase by electron doping<ref:2603.25742#pg2>. The existence of a distinct FL phase with small Fermi surface and the QCP are universal in systems with the U(1)t×U(1)b×SU(2)S/Z2 symmetry<ref:2603.25742#pg2>. This work provides a framework to understand the normal state of bilayer nickelates and related systems<ref:2603.25742#pg2>. The paper was supported by the National Science Foundation under Grant No. DMR2237031<ref:2603.25742#pg2>.

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Pseudogap Characteristics

The pseudogap behavior in the sFL phase is manifested as a divergent structure in the self-energy, approximated by Σ(ω) ∼ Φ 2/(ω + µψ)<ref:2603.25742#pg2>.

Improvements for AI systems

Improved phase diagram prediction for bilayer nickelates by tuning interlayer spin coupling J⊥ and hole doping x using single-site dynamical mean-field theory (DMFT). The improved system can predict whether a material is in a standard Fermi liquid or exhibits a pseudogap metal, specifically identifying the 'second Fermi liquid' (sFL) phase in the underdoped regime.
Enhanced understanding of strange metal behavior through mapping experimental observations to quantum critical points (QCPs). The improved system can correlate NFL behavior with specific bosonic operators like the total density and layer-alternating spin, suggesting that this NFL criticality is responsible for the strange metal behavior.
Development of a composite fermion framework for interpreting spectral functions in sFL phases. The improved system can interpret spectral features as arising from a spin polaron composite operator and demonstrate that this composite fermion dominates at low energy by showing a Kondo-like resonance peak in the spectral function of this composite fermion directly in DMFT calculation.
Precise characterization of Fermi surface reconstruction across phase transitions using topological indices. The improved system can use the Z2 index C = Qtot/2 (mod 2) to distinguish between FL and sFL phases, allowing it to predict a jump in the Fermi surface volume per flavor, DeltaAFS ±1/2 at the phase boundary.
Modeling of finite interlayer hopping effects on spectral features in bilayer systems. The improved system can analyze how finite t⊥ splits degenerate bands into alpha and beta bands and predict that the alpha band is gapped out by a divergent self-energy at omega = -10-4t rather than by a trivial interlayer hybridization t⊥ in mean field level.
Prediction of the stability of NFL criticality under symmetry breaking perturbations. The improved system can evaluate whether the QCP is stable for finite t⊥, concluding that the QCP likely evolves into a crossover for finite t⊥ but that the NFL regime controlled by the nearby QCP should still dominate the normal state above Tc.
Application of conformal field theory (CFT) to model quantum critical behavior near the two-impurity Anderson model. The improved system can use CFT fits to qualitatively capture NFL behavior near a QCP, showing that at criticality, Sasa = 0, corresponding to completely inelastic scattering.