Characterization of Thermalization Behaviour in a Generalized Aubry-Andr'e Model

arXiv:2604.25983 · quant-ph, cond-mat.dis-nn · Submitted 2026-04-28 · 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: "Characterization of Thermalization Behaviour in a Generalized Aubry-Andr'e Model".

Kai: The gist The study explores thermalization behavior in a generalized Aubry-Andr´e model with interacting spinless fermions using concepts like Frobenius norm of an adiabatic gauge potential to construct a phase…

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

Title and authors: Kai: So we’re diving into how this paper characterizes thermalization behavior in a generalized Aubry-Andr'e model. It’s authored by S. Mal, D. K. Nandy, and B. K. Sahoo at the Atomic, Molecular and Optical Physics Division in India, which is where we can actually run the kind of calculations they describe on real hardware to check out their findings later on.

Mira: The title itself points toward a deep look at how systems move from being ergodic—meaning they explore all possible states—to being localized when disorder gets strong enough, and it sets up a framework for understanding that transition in these complex models.

Lev: From an error correction standpoint, the authors are looking at how this localization happens in a model with interacting spinless fermions, which is relevant because those interactions are what you'd expect to see in many physical systems you want to make robust.

Kai: They’re using the concept of constructing a phase diagram through the Frobenius norm of an adiabatic gauge potential, which essentially lets them probe how sensitive the energy spectrum is to small changes in that quasi-periodic structure.

Mira: And they use that mapping to examine the stability of the critical disordered strength with respect to system size, which is a key way they try to figure out if their observed transition point actually holds up when you increase the system size.

The paper's summary: Kai: So what this paper does boils down to exploring the ergodic-to-many-body localization transition in this specific generalized Aubry-Andr'e model with interacting spinless fermions, using that gauge potential method we just talked about.

Mira: They are trying to build a phase diagram that captures the sensitivity of the eigenspectrum to small deformations in the adiabatic gauge potential, which is a way of seeing how disorder affects the system’s quantum state structure.

Lev: The paper sets up this model with kinetic energy and a site-dependent quasi-periodic modulation coefficient, and then they look at how interactions between spinless fermions influence that localization process.

Kai: They also provide some results in the non-interacting limit, showing a mobility edge described by the relation alpha E = two sgn(lambda)(t-lambda), which gives us a baseline for what happens before you even introduce those interactions <ref:2604.25983#pg2>.

Mira: Then they move on to numerical analysis using exact diagonalization for system sizes up to L=eighteen and use diagnostics like the adjacent gap ratio, defined as r i = (delta i+one delta i) / (delta i+one delta i), and the spectral form factor, which is a Fourier transform of the two-point correlation function in the eigenvalue spectra <ref:2604.25983#pg3>.

The paper's improvements: Kai: The paper points out that they can identify phase transitions by looking at indicators like when alpha=zero and V=one where they see a transition from an ergodic to a non-ergodic phase within the disorder range of one point four to one point nine, which hints at a critical disorder lambda* in that window.

Mira: They also assess the stability of this critical disorder by using cost-function minimization techniques applied to scaled fidelity susceptibility, which is a way to check if that transition point is robust against changes in system size.

Lev: And then they get into thermalization timescales, estimating the Thouless time t Th by examining the spectral form factor and find that its dependence on the GAA parameter can be substantial and even exceed the Heisenberg time t H.

Kai: They also observe that for the scaled fidelity susceptibility F, it exhibits a peak near the transition point, and this peak value drifts as system size increases, which is behavior similar to what we see in disordered spin systems.

Mira: Finally, they use finite-size scaling analysis through cost function minimization to show that for the fidelity susceptibility, this method gives a better data collapse for the power-law correlation length with linear drift compared to using other quantifiers.

Conclusion: Kai: So summarizing the whole thing, the paper concludes that while optimizing the adjacent gap ratio fits a BKT-type correlation length with a linear drift of critical disorder, cost function minimization for the fidelity susceptibility gives a better data collapse for that same power-law correlation length with linear drift.

Mira: They also find that this AGP prescription resembles a reduction in system size dependence on the critical value, especially for smaller values of alpha, which suggests increasing alpha suppresses ergodicity and favors MBL, making the system more susceptible to localized phases.

Lev: From my side, what sticks is how they’ve managed to optimize these diagnostics; it shows a pathway for running this kind of analysis on real hardware because it gives us better scaling behavior information.

Kai: Yeah, so the main implication is that increasing alpha pushes the system toward localization rather than thermalization, which directly relates to designing more robust quantum hardware where we want to avoid unwanted scrambling of information.

Mira: It really highlights how important it is to use these specific scaling analyses, like the cost function minimization for fidelity susceptibility, when you are trying to pinpoint the exact nature of a critical point in these disordered systems.

Lev: It’s useful because it gives us concrete metrics that show what we expect to see in the thermodynamic limit, rather than just looking at finite system sizes.

Kai: So we've covered the title, how they summarized their approach, and what they found about the stability of that critical strength. We’re going to wrap up this discussion on "Characterization of Thermalization Behaviour in a Generalized Aubry-Andr'e Model."

Atomic, Molecular and Optical Physics Division, Physical Research Laboratory

quant-ph, cond-mat.dis-nn

Submitted: 2026-04-28

Updated: 2026-10-08

Comments: 13 pages and 10 figures

Journal ref: Phys. Rev. B 114, 194201 (2026)

DOI: 10.1103/zh7f-2x1r

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

Importance score: 76/100

The gist: The gist The study explores thermalization behavior in a generalized Aubry-Andr´e model with interacting spinless fermions using concepts like Frobenius norm of an adiabatic gauge potential to

Key concepts

Generalized Aubry-Andr´e Model
This is a specific quantum model used to study how particles behave in systems with quasi-periodic potential. It includes kinetic energy, a site-dependent modulation coefficient, and nearest-neighbor interactions, allowing researchers to explore transitions between different physical states.
Many-Body Localization (MBL)
MBL is a phenomenon where interacting quantum systems remain localized even in the presence of disorder. The paper examines how the generalized Aubry-Andr´e model transitions into this non-ergodic, localized phase as certain parameters are changed, indicating suppressed thermalization.
Spectral Form Factor (SFF)
The SFF is a tool used to analyze the energy spectrum of the system. It's essentially a Fourier transform of the two-point correlation function between eigenvalues. Analyzing its behavior helps determine how quickly a system thermalizes or localizes.
Cost Function Minimization
This is a mathematical technique used to find optimal parameters that best fit experimental or numerical data. In this study, it was applied to scaled fidelity susceptibility to better characterize the critical disorder strength and the scaling behavior of correlation lengths.

Terminology

Summary

The gist The study explores thermalization behavior in a generalized Aubry-Andr´e model with interacting spinless fermions using concepts like Frobenius norm of an adiabatic gauge potential to construct a phase diagram and analyze the stability of the critical disordered strength

Model and Theoretical Framework

The research investigates the ergodic-to-many-body localization transition in the generalized Aubry-Andr´e model with interacting spinless fermions. The Hamiltonian for this model includes kinetic energy, a site-dependent quasi-periodic modulation coefficient, and nearest-neighbor interactions. The potential is defined by the expression Ci = 2 cos(2πqi+φ) / (1−α cos(2πqi+φ)), where α is a generalized AA parameter. In the non-interacting limit, the GAA model exhibits a mobility edge described by the relation αE = 2sgn(λ)(t−λ).

Numerical Analysis and Diagnostics

The study employs exact diagonalization (ED) for system sizes up to L = 18 to compute spectral properties. Key diagnostics used include the adjacent gap ratio, defined as ri = min(δi+1, δi) / max(δi+1, δi), and the spectral form factor (SFF), which is the Fourier transform of the two-point correlation function in the eigenvalue spectra. The analysis examines how these quantities behave across different disorder strengths and system sizes.

Phase Transition Characterization

The study identifies phase transitions by analyzing several indicators. For example, for α = 0 and V = 1, the system undergoes a transition from an ergodic to a non-ergodic phase within the disorder range 1.4 ≤ λ ≤ 1.9, indicating the critical disorder λ∗ between this range. The stability of the critical disorder is assessed through cost-function minimization techniques applied to scaled fidelity susceptibility.

Thermalization and Scaling Behavior

The thermalization timescale, known as the Thouless time (tTh), is estimated by examining the SFF, and findings indicate that its dependence on the GAA parameter is substantial and can even exceed the Heisenberg time (tH). The scaled fidelity susceptibility F exhibits a peak near the transition point, with this peak value drifting as system size increases, displaying behavior similar to that observed in disordered spin systems. The analysis of finite-size scaling using cost function minimization reveals that for the fidelity susceptibility, the cost function gives a better data collapse for the power-law correlation length with linear drift.

Conclusion on Critical Behavior

The study concludes that while the optimization of adjacent gap ratio shows a better fit for the BKT-type correlation length with a linear drift of critical disorder, cost function minimization for the fidelity susceptibility gives a better data collapse for the power-law correlation length with linear drift. The AGP prescription resembles a remarkable reduction in system-size dependence on the critical value, at least for lower values of α. The results suggest that increasing α suppresses ergodicity, favoring MBL and making the system more susceptible to localized phases.

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Atomic, Molecular and Optical Physics Division, Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India.

P. G. Department of Physics, S. K. C. G. (Auto.) College, Paralakhemundi, Odisha 761200, India.

S Ganeshan, J H Pixley, and S Das Sarma, Phys Rev Lett 114 146601 (2015).

D Sels and A Polkovnikov, Phys Rev E 104 054105 (2021).

Fig. 9. Critical point λ∗ as a function of system size L, for the power-law correlation ξ = ξ0 (left) and BKT-type correlation ξ = ξBKT (right) for different values of α.

Atomic, Molecular and Optical Physics Division, Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India.

P. G. Department of Physics, S. K. C. G. (Auto.) College, Paralakhemundi, Odisha 761200, India.

S Ganeshan, J H Pixley, and S Das Sarma, Phys Rev Lett 114 146601 (2015).

D Sels and A Polkovnikov, Phys Rev E 104 054105 (2021).

Fig. 9. Critical point λ∗ as a function of system size L, for the power-law correlation ξ = ξ0 (left) and BKT-type correlation ξ = ξBKT (right) for different values of α.

Atomic, Molecular and Optical Physics Division, Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India.

P. G. Department of Physics, S K C G (Auto.) College Paralakhemundi Odisha 761200 India.

S Ganeshan, J H Pixley, and S Das Sarma, Phys Rev Lett 114 146601 (2015).

D Sels and A Polkovnikov, Phys Rev E 104 054105 (2021).

Fig. 9. Critical point λ∗ as a function of system size L, for the power-law correlation ξ = ξ0 (left) and BKT-type correlation ξ = ξBKT (right) for different values of α.

Atomic, Molecular and Optical Physics Division, Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India.

P. G. Department of Physics S K C G (Auto.) College Paralakhemundi Odisha 761200 India.

S Ganeshan, J H Pixley, and S Das Sarma, Phys Rev Lett 114 146601 (2015).

D Sels and A Polkovnikov, Phys Rev E 104 054105 (2021).

Fig. 9. Critical point λ∗ as a function of system size L, for the power-law correlation ξ = ξ0 (left) and BKT-type correlation ξ = ξBKT (right) for different values of α.

Improvements for AI systems

  1. Bold header: Enhanced phase transition characterization in quasi-periodic systems. This improved AI system can accurately determine the stability of the critical disordered strength with respect to system size by performing a comprehensive data collapse analysis of the scaled χn and the adjacent gap ratio, employing cost-function minimization techniques.

  2. Bold header: Precise thermalization timescale estimation. The system can now estimate time scales using spectral diagnostics, as reported in the paper, such as examining the SFF to determine thermalization time scales, which can reveal behavior analogous to that observed in the strong disorder regime.

  3. Bold header: Discrimination between ergodic and MBL regimes via fidelity susceptibility. The improved system can utilize the scaling of the scaled fidelity susceptibility, F, to distinguish phases; specifically, it can observe that for a specific parameter set, the crossing of the three curves [in Fig. 5] specifies the transition λ∗ between ergodic and localized phases.

  4. Bold header: Prediction of critical disorder dependence on system size. The AI can predict the behavior of the critical disorder strength in the thermodynamic limit by analyzing finite-size scaling, noting that the cost function minimization for the fidelity susceptibility gives a better data collapse for the power-law correlation length with linear drift compared to other quantifiers.

  5. Bold header: Determination of correlation length type near transition. The system can compare different theoretical models by analyzing the data collapse of hri and F as function of L/ξ, allowing it to differentiate between the power-law type and BKT-type correlation lengths around the phase transition point.

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