Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2604.05997

Numerically Exact Study of Flat-Band Superconductivity

I. S. Tupitsyn, B. Currie, Boris V. Svistunov, Evgeny Kozik, Nikolay V. Prokof'ev

Published Apr 7, 2026• 0 citations
arXivHTMLPDF

Abstract

Current theories of high-temperature superconductivity in flat-band systems predict a linear dependence of the transition temperature on the attractive interaction, $T_c(U) = c|U|$. However, the value of $c$ and the full nonlinear $T_c(U)$ curve---with a maximum at large $|U|$---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 $U$, leading to a sharp crossover to long-range correlations at a characteristic temperature $T_*$, which provides a controlled upper bound on $T_c$. The highest $T_*$ occurs when all three bands touch at a single momentum point, potentially corresponding to high $T_c$ values.

DOI
10.48550/arxiv.2604.05997

Related papers

Superconducting transitions in flat-band systems

Vladimir Iglovikov, F. Hébert, Benoît Grémaud +2 more

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 $S$ 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.

arXiv:1404.5482•Physical Review B•Sep 11, 2014•111 citations

Pairing and superconductivity in the flat band: Creutz lattice

Rubem Mondaini, G. G. Batrouni, Benoît Grémaud

We use unbiased numerical methods to study the onset of pair superfluidity in a system that displays flat bands in the noninteracting regime. This is achieved by using a known example of flat band systems, namely, the Creutz lattice, where we investigate the role of local attractive interactions in the $U<0$ Hubbard model. Going beyond the standard approach used in these systems where weak interactions are considered, we map the superfluid behavior for a wide range of interaction strengths and exhibit a crossover between BCS and tightly bound bosonic fermion pairs. We further contrast these results with a standard two-leg fermionic ladder, showing that the pair correlations, although displaying algebraic decay in both cases, are longer ranged in the Creutz lattice, signifying the robustness of pairing in this system.

arXiv:1805.09359•Physical review. B./Physical review. B•Oct 25, 2018•69 citations

Emergent BEC mechanism in flat-band superconductors

V. Berger, I. S. Tupitsyn, B. Currie +3 more

The formation of bound bosonic pairs of fermions, followed by their Bose-Einstein (quasi) condensation (BEC), is a foundational mechanism of superconductivity. At low filling, flat-band superconductivity is well captured by this mechanism provided the flat band is separated from the occupied lower band by an energy gap. However, particularly high $T_c$ values are anticipated when the non-interacting flat and lower bands touch---as in the prototypical attractive Lieb-lattice model studied here---invalidating the conventional picture: while interactions might protect the bound state by opening a gap, no small parameter guarantees the separation of the bound-state energy from this gap or occupied-band excitations, leaving the pair's fate uncertain. Based on a controlled-precision numerical protocol---which we demonstrate to be essential in this fundamentally non-perturbative problem---we show that the BEC mechanism, underpinned by an interaction-induced gap, is generically robust and remarkably efficient: fermions doped into the flat band form bound pairs within this gap with an anomalously light effective mass, enabling an exceptionally high $T_c$.

arXiv:2608.19044•Aug 19, 2026•0 citations

Many-body superconductivity in topological flat bands

Jonah Herzog-Arbeitman, Aaron Chew, Kukka-Emilia Huhtinen +2 more

In a flat band superconductor, bosonic excitations disperse while unpaired electrons are immobile. To study this strongly interacting system, we construct a family of multi-band Hubbard models with exact eta-pairing ground states in all space groups. We analytically compute their many-body excitations and find that the Cooper pair bound states obey an effective single-boson hopping Hamiltonian written in terms of the non-interacting wavefunctions. These bound states possess a unique zero-energy excitation whose quadratic dispersion is determined by the minimal quantum metric. The rest of the bound state spectrum is classified by topological quantum chemistry, which we use to identify Cooper pairs with Weyl nodes, higher angular momentum pairing, and fragile topology. Broadening the band dispersion, we find the strongest pairing occurs at half filling and not at the highest density of states. Our analytical results prove that the elementary fermionic and bosonic excitations, corresponding respectively to pairing and coherence, are governed by distinct properties of the flat band, rigorously establishing its unique phenomenology. Superconductivity in flat bands is a central feature of quantum geometric effects, supported by mean-field theory and numerics. Here, the authors exhibit a large family of flat band Hubbard models whose ground states, Bogoliubov-de-Gennes particles, and Cooper pairs are exactly solvable with analytically calculable dispersions.

arXiv:2209.00007•Communications Physics•Jul 4, 2026•9 citations

Designer flat bands: Topology and enhancement of superconductivity

Si Min Chan, Benoît Grémaud, G. G. Batrouni

We construct quasi-one-dimensional topological and nontopological three-band lattices with a tunable band gap and winding number of the flat band. Using full multiband mean field (MF) and exact density matrix renormalization group (DMRG) calculations, we show explicitly how the band gap affects pairing and superconductivity (SC) in a Hubbard model with attractive interactions. We obtain excellent agreement between MF and DMRG calculations. The SC weight ${D}_{s}$ on the gapped topological, $W\ensuremath{\ne}0$, flat band increases linearly with interaction strength $U$ for low values and with a slope that depends on the details of the compact localized state at $U=0$. As $U\ensuremath{\rightarrow}0$ for the gapped nontopological flat band ($W=0$), ${D}_{s}$ decays with a power law faster than quadratically but slower than exponentially. In the gapless case (flat band touching the band above it), we find at low $U$ (for both $W=0$ and $W\ensuremath{\ne}0$) that ${D}_{s}\ensuremath{\propto}{U}^{\ensuremath{\varphi}}$, with $\ensuremath{\varphi}<1$. In other words, ${D}_{s}$ increases faster than linearly for low $U$, thus favoring SC at weak interaction more than the gapped case. Our results reestablish that the BCS mean field and quantum metric alone are insufficient to characterize SC at weak coupling.

arXiv:2206.10651•Physical review. B./Physical review. B•Sep 22, 2022•25 citations

Pairs, trimers, and BCS-BEC crossover near a flat band: Sawtooth lattice

Giuliano Orso, Manpreet Singh

We investigate pairing and superconductivity in the attractive Fermi-Hubbard model on the one-dimensional sawtooth lattice, which exhibits a flat band by fine-tuning the hopping rates. We first solve the two-body problem, both analytically and numerically, to extract the binding energy and the effective mass of the pairs. Based on the density matrix renormalization group method, we address the ground-state properties of the many-body system, assuming equal spin populations. We compare our results with those available for a linear chain, where the model is integrable by the Bethe ansatz, and we show that the multiband nature of the system substantially modifies the physics of the BCS-BEC crossover. We find that near a flat band, the chemical potential remains always close to its zero-density limit predicted by two-body physics. In contrast, the pairing gap exhibits a remarkably strong density dependence and, differently from the pair binding energy, it is no longer peaked at the flat-band point. We show that these results can be interpreted in terms of polarization screening effects, due to an anomalous attraction between pairs in the medium and single fermions. Importantly, we unveil that three-body bound states (trimers) exist in the sawtooth lattice, in sharp contrast with the linear chain geometry, and we compute their binding energy. The nature of these states is investigated via a strong-coupling variational approach, revealing that they originate from tunneling-induced exchange processes.

arXiv:2112.10188•Physical review. B./Physical review. B•Jul 6, 2022•10 citations
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.
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.
We use unbiased numerical methods to study the onset of pair superfluidity in a system that displays flat bands in the noninteracting regime. This is achieved by using a known example of flat band systems, namely, the Creutz lattice, where we investigate the role of local attractive interactions in the U<0U<0U<0 Hubbard model. Going beyond the standard approach used in these systems where weak interactions are considered, we map the superfluid behavior for a wide range of interaction strengths and exhibit a crossover between BCS and tightly bound bosonic fermion pairs. We further contrast these results with a standard two-leg fermionic ladder, showing that the pair correlations, although displaying algebraic decay in both cases, are longer ranged in the Creutz lattice, signifying the robustness of pairing in this system.
The formation of bound bosonic pairs of fermions, followed by their Bose-Einstein (quasi) condensation (BEC), is a foundational mechanism of superconductivity. At low filling, flat-band superconductivity is well captured by this mechanism provided the flat band is separated from the occupied lower band by an energy gap. However, particularly high TcT_cTc​ values are anticipated when the non-interacting flat and lower bands touch---as in the prototypical attractive Lieb-lattice model studied here---invalidating the conventional picture: while interactions might protect the bound state by opening a gap, no small parameter guarantees the separation of the bound-state energy from this gap or occupied-band excitations, leaving the pair's fate uncertain. Based on a controlled-precision numerical protocol---which we demonstrate to be essential in this fundamentally non-perturbative problem---we show that the BEC mechanism, underpinned by an interaction-induced gap, is generically robust and remarkably efficient: fermions doped into the flat band form bound pairs within this gap with an anomalously light effective mass, enabling an exceptionally high TcT_cTc​.
In a flat band superconductor, bosonic excitations disperse while unpaired electrons are immobile. To study this strongly interacting system, we construct a family of multi-band Hubbard models with exact eta-pairing ground states in all space groups. We analytically compute their many-body excitations and find that the Cooper pair bound states obey an effective single-boson hopping Hamiltonian written in terms of the non-interacting wavefunctions. These bound states possess a unique zero-energy excitation whose quadratic dispersion is determined by the minimal quantum metric. The rest of the bound state spectrum is classified by topological quantum chemistry, which we use to identify Cooper pairs with Weyl nodes, higher angular momentum pairing, and fragile topology. Broadening the band dispersion, we find the strongest pairing occurs at half filling and not at the highest density of states. Our analytical results prove that the elementary fermionic and bosonic excitations, corresponding respectively to pairing and coherence, are governed by distinct properties of the flat band, rigorously establishing its unique phenomenology. Superconductivity in flat bands is a central feature of quantum geometric effects, supported by mean-field theory and numerics. Here, the authors exhibit a large family of flat band Hubbard models whose ground states, Bogoliubov-de-Gennes particles, and Cooper pairs are exactly solvable with analytically calculable dispersions.
We construct quasi-one-dimensional topological and nontopological three-band lattices with a tunable band gap and winding number of the flat band. Using full multiband mean field (MF) and exact density matrix renormalization group (DMRG) calculations, we show explicitly how the band gap affects pairing and superconductivity (SC) in a Hubbard model with attractive interactions. We obtain excellent agreement between MF and DMRG calculations. The SC weight Ds{D}_{s}Ds​ on the gapped topological, $W\ensuremath{\ne}0$, flat band increases linearly with interaction strength UUU for low values and with a slope that depends on the details of the compact localized state at U=0U=0U=0. As $U\ensuremath{\rightarrow}0$ for the gapped nontopological flat band (W=0W=0W=0), Ds{D}_{s}Ds​ decays with a power law faster than quadratically but slower than exponentially. In the gapless case (flat band touching the band above it), we find at low UUU (for both W=0W=0W=0 and $W\ensuremath{\ne}0$) that ${D}_{s}\ensuremath{\propto}{U}^{\ensuremath{\varphi}}$, with $\ensuremath{\varphi}<1$. In other words, Ds{D}_{s}Ds​ increases faster than linearly for low UUU, thus favoring SC at weak interaction more than the gapped case. Our results reestablish that the BCS mean field and quantum metric alone are insufficient to characterize SC at weak coupling.
We investigate pairing and superconductivity in the attractive Fermi-Hubbard model on the one-dimensional sawtooth lattice, which exhibits a flat band by fine-tuning the hopping rates. We first solve the two-body problem, both analytically and numerically, to extract the binding energy and the effective mass of the pairs. Based on the density matrix renormalization group method, we address the ground-state properties of the many-body system, assuming equal spin populations. We compare our results with those available for a linear chain, where the model is integrable by the Bethe ansatz, and we show that the multiband nature of the system substantially modifies the physics of the BCS-BEC crossover. We find that near a flat band, the chemical potential remains always close to its zero-density limit predicted by two-body physics. In contrast, the pairing gap exhibits a remarkably strong density dependence and, differently from the pair binding energy, it is no longer peaked at the flat-band point. We show that these results can be interpreted in terms of polarization screening effects, due to an anomalous attraction between pairs in the medium and single fermions. Importantly, we unveil that three-body bound states (trimers) exist in the sawtooth lattice, in sharp contrast with the linear chain geometry, and we compute their binding energy. The nature of these states is investigated via a strong-coupling variational approach, revealing that they originate from tunneling-induced exchange processes.