Fermionic Spectral Functions in a Two-Current Gubser-Rocha Model with Axion Momentum Relaxation

arXiv:2610.11323 · hep-th, cond-mat.str-el · Submitted 2026-10-08 · 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: I'm Kai, and with me are Mira and Lev, guest researcher.

Mira: Today's paper: "Fermionic Spectral Functions in a Two-Current Gubser-Rocha Model with Axion Momentum Relaxation".

Kai: The gist The work investigates fermionic spectral functions in a two-current Gubser-Rocha background with linear-axion momentum relaxation to characterize how non-minimal fermion couplings reshape holographic fermionic excitations.

Mira: First, who's behind it and why it matters.

Paper summary: Kai: So we're looking at this paper, "Fermionic Spectral Functions in a Two-Current Gubser–Rocha Model with Axion Momentum Relaxation." Basically, the authors are using this setup—a two-current background with linear axion momentum relaxation—to see how non-minimal fermion couplings mess with those holographic excitations.

Mira: Exactly. The main thrust here is to show that these non-minimal couplings don't just produce simple gaps or simple features; they reshape the spectral functions in a really complex way, depending on what kind of coupling you have.

Lev: And from an error correction standpoint, if we were trying to model something real, this setup with momentum relaxation seems like a necessary step because it breaks that translational symmetry we need for clean quasiparticles <ref:2610.11323#pg3>.

Kai: Right, so the paper claims they look at three specific coupling channels—dipole, tensor, and vector—to see what happens. They use the dipole coupling as a baseline to show what you get without the more complex axion-dependent stuff.

Mira: That dipole coupling p1 produces a soft asymmetric reconstruction that doesn't actually open up a clean hard Mott gap, which is an important distinction from some earlier work <ref:2610.11323#pg3>. They find the zero-frequency spectral weight stays on a closed Fermi surface, but the Fermi momentum shifts outward as p1 increases.

Lev: If you were trying to build an error correction scheme based on this, that soft reconstruction suggests you're dealing with something more nuanced than just a simple gap opening <ref:2610.11323#pg2>.

Kai: Then they move onto the tensor coupling, p2. This one has a different effect; it suppresses that zero-energy Fermi peak and shifts the dominant spectral weight to higher frequencies, leading to what they call a flat-bottom reconstruction.

Mira: That flat bottom feature is linked to the tensor structure of mu nuH mu nu in the geometry <ref:2610.11323#pg2>. It's described as a background-modulated flat-bottom reconstruction, not a fully developed hard gap or just a flat band phase.

Lev: For hardware realization, having that spectral weight shift to finite frequencies sounds manageable compared to needing an infinite DC conductivity if we were using simpler geometries <ref:2610.11323#pg3>.

Kai: Next is the vector coupling, p3. This channel creates a strong asymmetry in momentum space, generating what they call open, Fermi-arc-like segments in the spectrum.

Mira: They quantify this by saying the integrated imbalance ratio RW increases rapidly with p3 and gets close to one at larger couplings, showing this one-sided redistribution of zero-frequency spectral weight <ref:2610.11323#pg2>. It comes from that axial-vector structure mu d mu psi I five <ref:2610.11323#pg2>.

Lev: A directional redistribution of spectral weight even though the axion background itself is homogeneous is interesting; it means the coupling structure dictates the directionality <ref:2610.11323#pg1>.

Kai: They also look at how changing the background parameters, specifically beta/mu and doping chi, affects these channels. The dependence gets more involved in the axion-related p2 and p3 channels because those interactions depend on the current mixing factor F alpha betaY alpha beta <ref:2610.11323#pg2>.

Mira: Specifically, increasing beta/mu generally broadens the p2 response, but for p3, that one-sided feature varies in a non-monotonic way as you change the background parameters <ref:2610.11323#pg1>. The paper shows that beta/mu and chi play different roles in reconstructing these spectra <ref:2610.11323#pg5>.

Lev: If we think about running this on actual quantum hardware, the fact that beta/mu broadens the response suggests we might need very precise control over those dissipation parameters to maintain coherence <ref:2610.11323#pg4>.

Kai: So, to recap the main point of "Fermionic Spectral Functions in a Two-Current Gubser–Rocha Model with Axion Momentum Relaxation," it's that the spectral reconstructions aren't just determined by the bare coupling constants you throw at it.

Mira: It’s sensitive to the dissipative two-current background too, which is what makes this study so interesting for understanding how non-minimal fermion couplings jointly reshape holographic excitations <ref:2610.11323#pg5>.

Lev: If you only listen to the show, think of it like this: we're looking at different ways a material can get stuck in different states because of its environment, not just the intrinsic material properties <ref:2610.11323#pg2>.

Kai: So for the conclusion, when we look at the paper's title and authors, Cai-E Liua and Defu Houa, this work really shows that the way you couple fermions to this geometry is deeply intertwined with how dissipative or relaxed your background is <ref:2610.11323#pg5>.

Mira: The authors highlight that the p2 channel gives a low-energy suppression paired with a shift of spectral weight to finite frequencies, while the p3 channel creates an asymmetric redistribution in momentum space <ref:2610.11323#pg5>. That's the core physical mechanism they found.

Lev: The implication is that these two different mechanisms—the low-energy suppression versus the momentum space asymmetry—are controlled jointly by the axion gradient and that mixed field-strength contraction <ref:2610.11323#pg5>.

Kai: And a limitation they mention is that momentum relaxation mainly broadens the spectral peaks and reduces their coherence <ref:2610.11323#pg5>, which means they can't fully resolve the sharpest features possible <ref:2610.11323#pg5>.

Mira: So, to wrap up, this paper confirms that we need to look at how the two-current Gubser–Rocha background itself dictates these spectral reconstructions, not just the bare coupling constants <ref:2610.11323#pg5>.

Lev: It's a good foundation for figuring out what kind of noise or dissipation you actually need to model when you're trying to build something that mimics this physics <ref:2610.11323#pg4>.

Conclusion: Kai: So, this paper is about how messing with the geometry—specifically this two-current Gubser-Rocha background—and adding linear axion momentum relaxation changes how fermions behave in a holographic system.

Mira: Yeah, they’re looking at those fermionic spectral functions and see exactly how those non-minimal couplings reshape the whole excitation picture.

Lev: From an error correction standpoint, I'm interested in how this geometry dictates the structure of the excitations you might want to use for encoding information.

Kai: The authors are Cai-E Liua and Defu Houa, and they show that we can get very different things depending on which coupling you use—dipole versus tensor versus vector.

Mira: That's the core finding, they demonstrate that the p2 channel gives you a low-energy suppression paired with spectral weight shifting to higher frequencies, resulting in a flat-bottom reconstruction.

Lev: And for hardware realization, that shift to finite frequencies sounds like it might be more manageable than needing infinite DC conductivity when you're trying to implement this in some kind of physical system.

Kai: Then they have the p3 vector channel, which creates a strong asymmetry in momentum space with what looks like open arcs in the spectrum.

Mira: They show that the integrated imbalance ratio for p3 goes up fast and gets close to one at larger couplings, confirming this one-sided redistribution of zero-frequency weight.

Lev: I wonder how you'd even measure that directional redistribution if you were trying to build a physical device with these features.

Kai: The paper concludes that the strength of this spectral deformation is controlled by the axion gradient and the mixed field-strength contraction, not just the bare coupling constants.

Mira: So, it’s not just about how strong you couple things directly; it’s also about how relaxed or dissipative your background geometry is <ref:2610.11323#pg5>.

Lev: That's a key distinction for me because if the geometry is too noisy or relaxed, it fundamentally changes the physics you are trying to model.

Kai: It basically says these spectral reconstructions aren't just determined by the coupling constants, but they’re sensitive to that dissipative two-current background itself.

Mira: The p2 channel does low-energy suppression with weight transfer, while p3 creates that momentum space asymmetry—those are the main results they highlight.

Lev: It suggests a complex interplay where you have competing effects from different coupling channels and the environment they're in.

Kai: Building on these results, the authors suggest a natural next step is to study what happens when both p2 and p3 interactions are present at the same time.

Mira: That would be interesting because we haven't seen how those two effects combine yet within this specific framework.

Lev: I'm looking forward to seeing if that combined scenario gives us a clearer picture of the overall structure of these excitations.

Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOS), Central China Normal University

hep-th, cond-mat.str-el

Submitted: 2026-10-08

Updated: 2026-10-08

Comments: 27 pages, 8 figures

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

Importance score: 82/100

The gist: The gist The work investigates fermionic spectral functions in a two-current Gubser-Rocha background with linear-axion momentum relaxation to characterize how non-minimal fermion couplings reshape

Key concepts

Two-Current Gubser–Rocha Background: This is a specific geometric setup used in holographic models that includes two U(1) gauge fields and an axion field. The axion field specifically implements momentum relaxation, meaning it causes the fermions to lose coherence or broaden their spectral peaks over distance.
Dipole Coupling (p1): This coupling acts as a comparison channel. It expands the existing Fermi surface without creating hard gaps, instead producing a soft reconstruction where the zero-energy spectral weight is redistributed around a closed ring, indicating a soft low-energy effect.
Tensor Coupling (p2): This channel suppresses the zero-energy Fermi peak and shifts the dominant spectral response to higher frequencies. It results in a flat-bottom reconstruction on the upper branch, which is linked to the tensor structure of the background geometry.

Terminology

Spectral Gap — 2× in this paper · explained in 5 episodes
AdS2 geometry — 1× in this paper · explained in 1 episode
Core — 1× in this paper · explained in 2 episodes
Nonminimal coupling — 1× in this paper · explained in 2 episodes
Particle-hole asymmetry — 1× in this paper · explained in 2 episodes
Symmetry Breaking — 1× in this paper · explained in 3 episodes
Unified Framework — 1× in this paper · explained in 5 episodes

Summary

The gist The work investigates fermionic spectral functions in a two-current Gubser-Rocha background with linear-axion momentum relaxation to characterize how non-minimal fermion couplings reshape holographic fermionic excitations.

Background Geometry and Setup

The study employs an extended two-current Einstein-Maxwell-Gubser–Rocha (EMGR) background containing linear axion fields that implement momentum relaxation, alongside two independent U(1) gauge fields that allow for a controllable doping parameter In this dissipative two-current background, the fermionic response is affected not only by the non-minimal coupling itself but also by the charge-sector mixing and the dissipative parameters of the geometry. The action used is S = Z d 4x √−g [R + 6 L2 cosh φ − α 4 e φFµνFµν − γ 4 e φYµνYµν (2.1) >

Dipole Coupling Response

The dipole coupling p1 serves as a comparison channel, producing a soft asymmetric reconstruction without opening a clean hard Mott gap. The zero-frequency spectral weight remains distributed along a closed Fermi surface, while the Fermi momentum shifts outward as p1 increases. The density of states develops a particle–hole-asymmetric profile as p1 increases, and DOS(0) shows a nonmonotonic dependence on p1 but remains finite over the parameter range considered. This behavior is described as a soft, particle–hole-asymmetric reconstruction reminiscent of the Mott-like behavior reported in holographic fermion systems.

Tensor Coupling (p2) Reconstruction

The tensor channel controlled by p2 suppresses the zero-energy Fermi peak and transfers the dominant spectral response to finite frequencies, resulting in a flat-bottom reconstruction. The upper spectral branch develops a pronounced flat-bottom feature, which is associated with the tensor structure ΓµνHµν. This behavior is characterized as a background-modulated flat-bottom reconstruction, distinct from fully developed hard gaps or flat-band phases.

Vector/Axion-Gradient Coupling (p3) Reconstruction

The vector channel controlled by p3 creates a strong spectral asymmetry in momentum space, generating open, Fermi-arc-like segments. The integrated imbalance ratio RW increases rapidly with p3 and approaches unity at larger coupling, confirming an increasingly one-sided redistribution of the zero-frequency spectral weight. This asymmetry originates from the axial-vector structure (Γµ∂µψI)Γ5, which affects the two momentum branches differently and produces a directional redistribution of spectral weight even though the axion background remains homogeneous.

Dependence on Background Parameters

The dependence on the background parameters β/µ and χ becomes more involved in the axion-related p2 and p3 channels, as these interactions depend explicitly on the axion sector and are modulated by the current-mixing factor FαβYαβ. Momentum relaxation mainly broadens the spectral peaks and reduces their coherence, while doping primarily shifts the characteristic momentum scale through the charge-sector background. For p2, these effects weaken the contrast of the symmetric low-energy suppression, whereas for p3, they tune the one-sided spectral segment in a non-monotonic manner. These results show that β/µ and χ play different roles in the reconstructed spectra.

Conclusion

The spectral reconstructions induced by the non-minimal couplings are not determined solely by the bare coupling constants, but are also sensitive to the dissipative two-current background. The p2 channel produces low-energy suppression accompanied by spectral-weight transfer to finite frequencies, while the p3 channel produces an asymmetric redistribution of spectral weight in momentum space. The distinctive feature of the present construction is that the strength of this deformation is controlled jointly by the axion gradient and the mixed field-strength contraction. Building on these results, a natural next step is to study the interplay between the p2 and p3 interactions when both are present. The paper concludes by noting that momentum relaxation mainly broadens spectral peaks and reduces coherence, while doping primarily shifts the characteristic momentum scale through the charge-sector background. The results confirm that these reconstructions are controlled by the dissipative two-current Gubser–Rocha background.

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Fermionic Spectral Functions in a Two-Current Gubser–Rocha Model with Axion Momentum Relaxation

Cai-E Liua and Defu Houa,1

Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOS), Central China Normal University, Wuhan 430079, China

E-mail: liucaie88@mails.ccnu.edu.cn, houdf@mail.ccnu.edu.cn

Abstract: We investigate fermionic spectral functions in a two-current Gubser-Rocha background with linear-axion momentum relaxation Serving as a comparison channel, the dipole coupling p1 is found to produce a soft asymmetric reconstruction without opening a clean hard Mott gap. Our main analysis then focuses on two axion-dependent nonminimal couplings modulated by current mixing. The p2 tensor channel suppresses the zero-energy Fermi peak and shifts the dominant spectral weight to finite frequencies, resulting in a flat-bottom reconstruction. In contrast, the p3 vector channel creates a strong spectral asymmetry in momentum space, generating open, Fermi-arc-like segments. Varying the momentum-relaxation strength β/µ and the doping parameter χ reveals a channeldependent response to the two-current background Increasing β/µ generally broadens the p2 response, whereas the one-sided p3 feature varies non-monotonically under changes of the background parameters These results clarify how current mixing, axion-induced momentum relaxation, and non-minimal fermion couplings jointly reshape holographic fermionic excitations.

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4.1 Interaction-Induced Spectral Reconstruction

We first examine the dipole coupling p1, which serves as a comparison channel for the axion-related interactions. Figure 2 shows the zero-frequency spectral density A(kx, ky) and the corresponding dispersion relation A(ω, kx) for p1 = 2, 4, 8. As p1 increases, the zero-energy spectral weight remains distributed along a closed Fermi ring, while the ring radius increases. Thus, the dipole coupling expands the Fermi surface but does not break it into open segments. The dispersion plots show an asymmetric redistribution of spectral weight around the Fermi level, indicating a soft reconstruction of the low-energy spectrum. Exploiting the rotational symmetry of the clean background, we evaluate the density of states as DOS(ω) = 1 / 2π Z kmax 0 dk k A(ω, k).

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Figure 2: Density plots of the spectral function A(kx, ky) at ω = 0 (odd columns) and dispersion relations A(ω, kx) along ky = 0 (even columns). Fixed parameters are mψ = 0, q = 1, χ = 1.0, and T /µ = 0.009 in the clean limit (β/µ = 0). Panels (a)–(f) present the spectral evolution with dipole coupling strengths p1 = 2, 4, and 8.

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Figure 3: Spectral functions for different values of the dipole coupling p1. (a) Momentumintegrated density of states DOS(ω). (b) Zero-energy momentum cuts ImG22(kx) at ω = 0. (c) Zero-frequency density of states DOS(0) as a function of p1. Other parameters are fixed as mψ = 0, q = 1, χ = 1.0, and β/µ = 0. The finite and non-monotonic DOS(0) suggests a soft low-energy suppression rather than a hard gap.

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Figure 4: Density plots of the spectral function A(kx, ky) at ω = 0 (odd columns) and dispersion relations A(ω, kx) along ky = 0 (even columns). Fixed parameters are mψ = 0, q = 1, χ = 1.0, and T /µ = 0.009 with finite momentum relaxation (β/µ = 0.4). The top row (a)–(f) presents the spectral evolution driven by the tensor coupling p2 set to 0.2, 0.4, and 0.8, showing the band flattening effect. The bottom row (g)–(l) corresponds to the vector coupling p3 set to 0.2, 0.5, and 0.8, respectively, showing arc-like spectral redistribution.

Improvements for AI systems

The improved system can perform high-fidelity spectral reconstruction analysis by explicitly distinguishing between p2 and p3 channels, as described in The tensor channel controlled by p2 suppresses the zero-energy Fermi peak and shifts the dominant spectral weight to finite frequencies, resulting in a flat-bottom reconstruction versus the vector channel controlled by p3 creates a strong spectral asymmetry in momentum space, generating open, Fermi-arc-like segments.
The system can quantitatively assess the tuning effects of background parameters by analyzing how they tune the dipole-channel spectrum in different ways, specifically noting that for p2, momentum relaxation mainly broadens and weakens the spectral peaks, while for p3, it produces a non-monotonic tuning of the one-sided spectral peak.
The improved system can predict the non-monotonic dependence of spectral weight by modeling how background parameters affect the p2 and p3 channels, specifically observing that for p2, momentum relaxation weakens the contrast of the symmetric low-energy suppression, while for p3, it causes a non-monotonic tuning of the one-sided spectral peak.
The system can differentiate between different physical origins of spectral features by comparing them to established holographic models; for instance, it can distinguish that the p2 response is mainly affected through the broadening and weakening of its symmetric low-energy structure versus the p3 channel produces a one-sided spectral feature that is tuned more sensitively and non-monotonically by the dissipative two-current background.