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arXiv:2605.26231

Competition between pair and single-particle superfluidity in bosonic quasi-flat bands: A Gaussian state approach

Maxime Burgher, Simon Loddo, Laurens Vanderstraeten, Nathan Goldman, Ivan Amelio

Published May 25, 2026• 0 citations
arXivHTMLPDF

Abstract

The interplay between interactions and quantum geometry can drive weakly dispersive bosons into different exotic many-body phases. In this work we study a quasi flat-band model in one dimension that exhibits an extended pair-superfluid phase in the all-flat-band limit. Introducing single-particle hopping leads to an intriguing competition with a more conventional single-particle superfluid: we find that the pair superfluid remains stable for a finite range of the hopping strength until the system eventually transitions into the conventional superfluid phase. In our study, we make use of a variational Gaussian state approach that provides a unified description of the single-particle and pair superfluid phases, regarding both the ground state wavefunction and the collective excitation spectrum. In particular, we derive a general relation between the speed of sound and a ``quantum geometric kernel'', thereby extending earlier connections to the quantum metric, which relied on single-particle mean-field theory. This approach is combined with insights from the two-boson problem and exact diagonalization to map out the full phase diagram of the model. Our results show that the Gaussian approach is a versatile tool for studying a broad range of superfluid phases of interacting bosons in multi-orbital lattices.

DOI
10.48550/arxiv.2605.26231

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The interplay between interactions and quantum geometry can drive weakly dispersive bosons into different exotic many-body phases. In this work we study a quasi flat-band model in one dimension that exhibits an extended pair-superfluid phase in the all-flat-band limit. Introducing single-particle hopping leads to an intriguing competition with a more conventional single-particle superfluid: we find that the pair superfluid remains stable for a finite range of the hopping strength until the system eventually transitions into the conventional superfluid phase. In our study, we make use of a variational Gaussian state approach that provides a unified description of the single-particle and pair superfluid phases, regarding both the ground state wavefunction and the collective excitation spectrum. In particular, we derive a general relation between the speed of sound and a ``quantum geometric kernel'', thereby extending earlier connections to the quantum metric, which relied on single-particle mean-field theory. This approach is combined with insights from the two-boson problem and exact diagonalization to map out the full phase diagram of the model. Our results show that the Gaussian approach is a versatile tool for studying a broad range of superfluid phases of interacting bosons in multi-orbital lattices.
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Superconductivity in a partially filled flat band presents a vexing conceptual hurdle because the absence of a Fermi surface precludes a weak-coupling regime where one can extend insights from the Bardeen-Cooper-Schrieffer picture of a Fermi surface instability. We approach the strongly correlated problem of flat band superconductivity from the strong coupling limit of local attractive interactions on line-graph lattices, whose non-interacting bandstructures host exactly flat bands due to frustrated hopping. In this limit, the pair kinetic energy which sets the superfluid stiffness is expected to scale inversely with the pair binding interaction. Here we demonstrate a striking counterexample. We show that when doped charges propagate on the line-graph of a lattice with strong pairing interaction and broken time-reversal symmetry, they bind into obstructed Cooper pairs whose motion is frustrated by destructive interference. As a result, the leading-order pair kinetic energy vanishes identically in the strong-coupling expansion, producing a flat bosonic band of compact localised pair states, zero superfluid stiffness at leading order, and an extensively degenerate many-body ground state manifold. At quarter filling, the frustrated pair dynamics maps onto a quantum dimer model which has a ddd-wave resonating-valence-bond ground state when time-reversal is broken. The pairing Hamiltonian in this limit thus has a topologically ordered spin liquid ground state which becomes exact at the analytically solvable Rokhsar-Kivelson point with long-range entanglement and deconfined holon excitations. Interestingly, we find exact compact localised eigenstates and extensive degeneracies in the many-body eigenstates of this emergent dimer model. Our results establish a disorder-free mechanism for interaction-driven localisation, in which strong pairing collapses the kinetic energy of Cooper pairs.
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.
We investigate collective excitations in flat-band superfluids by incorporating the coupled dynamics of pairing (phase and amplitude) and density fluctuations. We demonstrate that for any time-reversal symmetric superfluid system with an isolated flat band, only a single low-energy collective mode emerges in the long-wavelength limit. In contrast to the linearly dispersive Goldstone mode in conventional superfluids, this hybridized mode is gapless at zero momentum but exhibits a quadratic dispersion (ω∝q2ω\propto q^2ω∝q2) at small momenta. We show that the dispersion coefficients of this collective mode are governed by the normal-state quantum metric of the flat band. These analytical predictions are in excellent agreement with numerical calculations. Our results are applicable to any generic sss-wave flat-band superfluid, provided the flat band is energetically well separated from other dispersive bands.
Abstract We investigate theoretically the superfluidity of a one-dimensional boson system whose hopping energy is periodically modulated with a zero time average, which results in the suppression of first-order single-particle hopping processes. The dynamics of this Floquet-engineered flat-band system is entirely driven by correlations and described by exotic Hamiltonian and current operators. We employ exact diagonalization and compare our results with those of the conventional, undriven Bose–Hubbard system. We focus on the two main manifestations of superfluidity, the Hess-Fairbank effect and the metastability of supercurrents, with explicit inclusion of an impurity when relevant. Among the novel superfluid features, we highlight the presence of a cat-like ground state, with branches that have opposite crystal momentum but carry the same flux-dependent current, and the essential role of the interference between the collective components of the ground-state wave function. Calculation of the dynamic form factor reveals the presence of an acoustic mode that guarantees superfluidity in the thermodynamic limit.
We consider the superfluid weight, speed of sound and excitation fraction of a flat band Bose–Einstein condensate (BEC) within multiband Bogoliubov theory. The superfluid weight is calculated by introducing a phase winding and minimizing the free energy with respect to it. We find that the superfluid weight has a contribution arising from the change in the condensate density and chemical potential upon the phase twist that has been neglected in the previous literature. We also point out that the speed of sound and the excitation fraction are proportional to orbital-position-independent generalizations of the quantum metric and the quantum distance, and reduce to the usual quantum metric (Fubini–Study metric) and the Hilbert–Schmidt quantum distance only in special cases. We derive a second-order perturbation correction to the dependence of the speed of sound on the generalized quantum metric, and show that it compares well with numerical calculations. Our results provide a consistent connection between flat band BEC and quantum geometry, with physical observables being independent of the orbital positions for fixed hopping amplitudes, as they should, and complete formulas for the evaluation of the superfluid weight within the Bogoliubov theory. We discuss the limitations of the Bogoliubov theory in evaluating the superfluid weight.