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arXiv:2610.34342

Fermionic superfluid transition and pairing scale separation in the kagome flat band

Xiang Li, Yu Wang

Published Oct 25, 2026• 0 citations
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Abstract

Flat-band systems provide a promising platform for exploring exotic correlated phases owing to quenched kinetic energy and enhanced interaction effects. In this work, we investigate the flat-band superfluid transition in the attractive kagome Hubbard model using large-scale determinant quantum Monte Carlo simulations accelerated by fast Fourier transforms and delay updates. Through systematic calculations of the transition temperature, spin susceptibility, and density compressibility, we establish the finite-temperature phase diagram at the flat-band filling $ρ=5/3$ and find a clear linear scaling of the superfluid transition temperature with the interaction strength, $T_{\mathrm{c}}=0.0314|U|$. Our results reveal a wide separation of temperature scales between local pair formation and global phase coherence, which stabilizes a broad intermediate supercompressible bosonic fluid region of preformed pairs that bridges the normal Fermi gas and the flat-band superfluid. We further demonstrate that both the transition temperature and density compressibility are significantly enhanced in the flat band compared to van Hove fillings. Our findings highlight the essential role of flat-band-enhanced pair-density fluctuations in separating the pairing and phase-coherence scales, offering clear experimental signatures for probing flat-band superfluidity and superconductivity in cold-atom and kagome-material platforms.

DOI
10.48550/arxiv.2610.34342

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Flat-band systems provide a promising platform for exploring exotic correlated phases owing to quenched kinetic energy and enhanced interaction effects. In this work, we investigate the flat-band superfluid transition in the attractive kagome Hubbard model using large-scale determinant quantum Monte Carlo simulations accelerated by fast Fourier transforms and delay updates. Through systematic calculations of the transition temperature, spin susceptibility, and density compressibility, we establish the finite-temperature phase diagram at the flat-band filling ρ=5/3ρ=5/3ρ=5/3 and find a clear linear scaling of the superfluid transition temperature with the interaction strength, Tc=0.0314∣U∣T_{\mathrm{c}}=0.0314|U|Tc​=0.0314∣U∣. Our results reveal a wide separation of temperature scales between local pair formation and global phase coherence, which stabilizes a broad intermediate supercompressible bosonic fluid region of preformed pairs that bridges the normal Fermi gas and the flat-band superfluid. We further demonstrate that both the transition temperature and density compressibility are significantly enhanced in the flat band compared to van Hove fillings. Our findings highlight the essential role of flat-band-enhanced pair-density fluctuations in separating the pairing and phase-coherence scales, offering clear experimental signatures for probing flat-band superfluidity and superconductivity in cold-atom and kagome-material platforms.
Kagome metals exhibit a rich interplay of topology, electronic correlations, and lattice dynamics. Recent discoveries of Kagome materials with a flat band near the Fermi level have revealed a variety of correlated electronic phases. However, elucidating their microscopic origin remains challenging, as realistic descriptions require accounting for multiple orbitals and competing interactions on an equal footing. To disentangle correlation effects from material-specific details and identify the essential physics of the flat-band regime, we study the single-orbital Kagome-Hubbard model at flat-band fillings using dynamical mean-field theory. We find strong signatures of flat-band ferromagnetism, consistent with exact and mean-field ground-state results. Moreover, we uncover an unconventional quasi-ordered phase in which a partially filled spin-polarized flat band pinned at the Fermi level gives rise to persistent local spin fluctuations down to zero temperature, in striking contrast to the classical behavior expected for a conventional ferromagnet. Our results demonstrate that these anomalous fluctuations are an intrinsic consequence of the flat-band degeneracy and establish a minimal framework for understanding correlation effects in flat-band Kagome systems.
The Kagome lattice Fermi-Hubbard model is one of the most physically rich, and at the same time most challenging, models to study in strongly-correlated physics. Among its special features are geometric frustration and a flat energy band that create conditions favorable to ferromagnetism near the band insulating limit. Here, we utilize two exact finite-temperature methods, the numerical linked-cluster expansion and the determinant quantum Monte Carlo, to study the extent as well as doping and interaction dependence of ferromagnetic correlations and other thermodynamic properties of the model. We find that repulsive interactions enhance ferromagnetic correlations at high electron densities and that increasing the interaction strength, extends the region with strong ferromagnetic correlations towards half filling, smoothly connecting it to Nagaoka ferromagnetism near the Mott insulating region. We also use the charge compressibility to obtain an accurate estimate for the critical interaction strength for the metal-insulator transition at half filling. These results improve our understanding of the magnetic tendencies of the model away from half filling and pave the way for further studies, including with ultracold atoms in optical lattices.
Current theories of high-temperature superconductivity in flat-band systems predict a linear dependence of the transition temperature on the attractive interaction, Tc(U)=c∣U∣T_c(U) = c|U|Tc​(U)=c∣U∣. However, the value of ccc and the full nonlinear Tc(U)T_c(U)Tc​(U) curve---with a maximum at large ∣U∣|U|∣U∣---are known beyond mean-field and quantum geometry estimates only for systems with isolated flat bands. Using a controlled diagrammatic Monte Carlo technique, we trace the onset of superfluid response in the Lieb lattice with attractive Hubbard interaction. Focusing on the half-filled flat-band case, where the ordering mechanism differs fundamentally from both BCS and BEC (preformed Cooper pair) scenarios, we find that the pairing response diverges linearly with decreasing temperature over a broad range of UUU, leading to a sharp crossover to long-range correlations at a characteristic temperature T∗T_*T∗​, which provides a controlled upper bound on TcT_cTc​. The highest T∗T_*T∗​ occurs when all three bands touch at a single momentum point, potentially corresponding to high TcT_cTc​ values.
We study the attractive Hubbard model with spin imbalance on two lattices featuring a flat band: the Lieb and kagome lattices. We present mean-field phase diagrams featuring exotic superfluid phases, similar to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, whose stability is confirmed by dynamical mean-field theory. The nature of the pairing is found to be richer than just the Fermi surface shift responsible for the usual FFLO state. The presence of a flat band allows for changes in the particle momentum distributions at null energy cost. This facilitates formation of nontrivial superfluid phases via multiband Cooper pair formation: the momentum distribution of the spin component in the flat band deforms to mimic the Fermi surface of the other spin component residing in a dispersive band. The Fermi surface of the unpaired particles that are typical for gapless superfluids becomes deformed as well. The results highlight the profound effect of flat dispersions on Fermi surface instabilities, and provide a potential route for observing spin-imbalanced superfluidity and superconductivity.
Taking cue from the recent experimental realization of metallic phases in Kagome materials we report the low temperature signatures and thermal scales of Kagome metals and insulators, determined in the framework of the Kagome Hubbard model, using a non perturbative numerical approach. In contrast to the existing consensus we establish a flat band localized insulator in the weak coupling regime which crosses over to a non Fermi liquid (NFL) metal at intermediate coupling, followed by a first order metal-Mott insulator transition in the strong coupling regime. We provide the first accurate estimates of the thermal scales of this model and analyze the NFL phases in terms of resilient quasiparticles and short range magnetic correlations. With our unprecedented access to the low temperature phases and sufficiently large system sizes, we provide the essential benchmarks for the prospective experiments on the Kagome metal and insulators in terms of their thermodynamic, spectroscopic and transport signatures.
The physics of strongly correlated quantum particles within a flat band was originally explored as a route to itinerant ferromagnetism and, indeed, a celebrated theorem by Lieb rigorously establishes that the ground state of the repulsive Hubbard model on a bipartite lattice with an unequal number of sites in each sublattice must have nonzero spin SSS at half filling. Recently, there has been interest in Lieb geometries due to the possibility of topological insulator, nematic, and Bose-Einstein condensed (BEC) phases. In this paper, we extend the understanding of the attractive Hubbard model on the Lieb lattice by using determinant quantum Monte Carlo to study real space charge and pair correlation functions not addressed by the Lieb theorems. Specifically, our results show unusual charge and charge transfer signatures within the flat band, and a reduction in pairing order at $\ensuremath{\rho}=2/3$ and $\ensuremath{\rho}=4/3$, the points at which the flat band is first occupied and then completely filled. We compare our results to the case of flat bands in the Kagome lattice and demonstrate that the behavior observed in the two cases is rather different.