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Attenuating Dynamics of Strongly Interacting Fermionic Superfluids in SYK Solvable Models

by Tian-Gang Zhou, Pengfei Zhang

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Submission summary

Authors (as registered SciPost users): Pengfei Zhang
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-07-24
Date submitted: 2023-07-13 05:32
Submitted by: Zhang, Pengfei
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


Quench dynamics of fermionic superfluids are an active topic both experimentally and theoretically. Using the BCS theory, such non-equilibrium problems can be reduced to nearly independent spin dynamics, only with a time-dependent mean-field pairing term. This results in persisting oscillations of the pairing strength in certain parameter regimes. However, experiments have observed that the oscillations decay rapidly when the interaction becomes strong, such as in the unitary Fermi gas. Theoretical analysis on this matter is still absent. In this work, we construct an SYK-like model to analyze the effect of strong interactions in a one-dimensional BCS system. We employ the large-$N$ approximation and a Green's function-based technique to solve the equilibrium problem and quench dynamics. Our findings reveal that a strong SYK interaction suppresses the pairing order. Additionally, we verify that the system quickly thermalizes with SYK interactions, whether it involves intrinsic pairing order or proximity effect, resulting in a rapid decay of the oscillation strength. The decay rates exhibit different scaling laws against SYK interaction, which can be understood in terms of the Boltzmann equation. This work represents a first step towards understanding the attenuating dynamics of strongly interacting fermionic superfluids.

Author comments upon resubmission

We are delighted to observe that both referees find our work interesting and recommend its publication after appropriate revision. In this revision, we have made several improvements based on their suggestions:

1). In accordance with the suggestion mentioned in both Report 1 (question 1), we have added discussions on the motivation of our Hamiltonian in section 2. We state the following:
“There are two reasons for considering Eq. (1). Firstly, it provides a concrete model for studying superconductors with strong interactions, allowing for investigations into both equilibrium properties and quantum dynamics within the large-$N$ limit. Secondly, it is known that the original SYK model exhibits non-Fermi liquid behavior, with its low-energy manifold being dual to the Jackiw–Teitelboim gravity theory in 1+1-D. By generalizing this model to higher dimensions, it becomes a valuable tool for understanding strongly correlated materials. Therefore, our model sheds light on the understanding of superconductivity in higher-dimensional non-Fermi liquids. Recently, several works have also proposed similar constructions for the superconductivity SYK model, albeit in different dimensionality or with correlated SYK interactions through Yukawa interaction with soft boson.”

2). Regarding question 2 of Report 1, we confirm that the intercell disorder average <…> is taken with respect to N, which means modes number in a single site. But momentum summation is always associated with the number of sites N_s. We realized that our previous text may have led to confusion. In this revision, we have rephrased the sentence to improve clarity.

3). Regarding question 3 of Report 1, equation (11) is exactly the leading-order contribution in the large-N limit, similar to the original SYK model. We realized that our previous statement about melon diagrams was confusing. In the revised version, we directly state "using Eq. (11)" instead of "using the melon diagram approximation" in section 2.2.

4). As suggested in both Report 1 (question 4), we have added references for the cold atom experiment and the first statement in the first paragraph of section 3.1.

5). Following the suggestions in both Report 1 (question 5) and Report 2, we have expanded the explanation for different scalings of the decay rate against the SYK interaction using the semiclassical Boltzmann equation in section 3.2.

6). In line with the suggestion in Report 2, we have checked the spelling, grammar, and corrected a few typos throughout the manuscript. Specifically, we have rewritten part of the abstract to improve clarity.

7). Building upon the suggestion in Report 2, we have added discussions on the attenuated pairing in section 3.1. We explain, "This can be understood as the SYK interaction introduces a finite lifetime for fermions near the Fermi surface at a fixed temperature $T$. Consequently, it diminishes the pairing instability near the Fermi surface and leads to an increase in the critical BCS interaction $g_c$."

List of changes

1. We added discussions for the motivation of the Hamiltonian.
2. We rephrased the sentence for the disorder average to improve clarity.
3. We rephrased the statement on melon diagrams.
4. We added references for the cold atom experiment.
5. We expanded the explanation for different scalings of the decay rate.
6. We improved the grammar throughout the manuscript and rewrite the abstract.
7. We added discussions for the attenuated paring.

Published as SciPost Phys. 15, 108 (2023)

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