Attractive Hubbard Model Research Articles

Disentangling the physics of the attractive Hubbard model as a fully interacting model of fermions via the accessible and symmetry-resolved entanglement entropies

Disentangling the physics of the attractive Hubbard model as a fully interacting model of fermions via the accessible and symmetry-resolved entanglement entropies

Hidden symmetry of Bogoliubov de Gennes quasi-particle eigenstates and universal relations in flat band superconducting bipartite lattices

Unconventional flat band (FB) superconductivity, as observed in van der Waals heterostructures, could open promising avenues towards high-T_cc materials. In FBs, pairings and superfluid weight scale linearly with the interaction parameter, such an unusual behaviour justifies and encourages strategies to promote FB engineering. Bipartite lattices (BLs) which naturally host FBs could be particularly interesting candidates. Within Bogoliubov de Gennes theory and in the framework of the attractive Hubbard model in BLs, a hidden symmetry of the quasi-particle eigenstates is revealed. As a consequence, we demonstrate universal relations for the pairings and the superfluid weight that are independent of the characteristics of the hopping term. Remarkably, it is shown that these general properties are insensitive to disorder as long as the bipartite character is protected.

Work Statistics and Entanglement Across the Fermionic Superfluid‐Insulator Transition

AbstractEntanglement in many‐body systems may display quantum phase transition signatures, and analogous insights are emerging in the study of work fluctuations. Here, the fermionic superfluid‐to‐insulator transition (SIT) is considered and related to its entanglement properties and its work distribution statistics. Using the attractive fermionic Hubbard model with randomly distributed impurities, the work distribution is analyzed under two quench protocols triggering the SIT. In the first, the concentration of impurities is increased; in the second, the impurities' disorder strength is varied. The results indicate that, at criticality, the entanglement is minimized while the average work is maximized. This study demonstrates that, for this state, density fluctuations vanish at all orders, resulting in all central moments of the work probability distribution being precisely zero. For systems undergoing a precursor to the transition (short chains with finite impurity potential) numerical results confirm these predictions, with higher moments further from the ideal results. For both protocols, at criticality, the system absorbs the most energy with almost no penalty in terms of fluctuations: ultimately this feature can be used to implement a quantum critical battery. The impact of temperature on this critical behaviour is also investigated and shown to favor work extraction for high enough temperatures.

Superconductivity in correlated carbon nanotubes under pressure: A Bogoliubov-de Gennes study

In contrast to most microscopic theories of superconductivity based on the reciprocal space, the Bogoliubov-de Gennes (BdG) formalism provides a real-space alternative for addressing inhomogeneous systems. In this article, we study the superconducting states in correlated single-walled carbon nanotubes (SWNTs) with curvature and spin-orbit corrections, as well as the inter-tube interaction through a connecting molecule using an attractive Hubbard model. The results reveal a close relationship between the on-site superconducting gap and the single-electron local density of states. For the limiting case of independent large-diameter nanotubes, the BdG equations can be reduced to the standard Bardeen-Cooper-Schrieffer one with analytical solutions. Moreover, an optimal separation between nanotubes is found, which leads to a maximal superconducting critical temperature. This finding has a remarkable accordance with the experimental data obtained from Buckypapers built of boron doped SWNTs under external pressure.

Superconductivity of metallic graphene

It has been found that the states at the level of the Fermi energy of undoped graphene sheet reduces to zero, making it difficult for the Cooper pairing of such a system to exist in its superconductive state. Instead, T-graphene, having physical properties close to graphene, exhibits a metallic behavior which means the existence of the available states for electrons near to Fermi level. For this two-dimensional metallic system, the gap equation of the s-wave superconductive state is derived based on the Bogoliubov de Gennes equation within the attractive Hubbard model. Using the gap equation, a nonzero critical temperature, Tc, is found for different amounts of electron–electron interaction, U. Tc has higher values when the system possesses electronic half band-filling, whereas the reverse is true when the system does not have half band-filling. However, close to band edges, Tc vanishes when U becomes small enough.

Role of inter-site Coulomb interaction on the thermodynamic and ground state properties within the [formula omitted] model

In this work, we report the effect of nearest neighbor (NN) inter-site Coulomb interaction (V) with a certain finite value of on-site Coulomb repulsion (U) and NN antiferromagnetic exchange interaction (J) in the context of high-Tc cuprates. An exact diagonalization method has been applied in a 2D t−J−U model extended by NN inter-site Coulomb interaction in the tilted square cluster near optimal doping. The antiferromagnetic tendency is suppressed by the inter-site e−e repulsion. The inter-site Coulomb repulsion produces an effective on-site attraction between electrons, resulting in the creation of doublons against the on-site Coulomb repulsion. The computation of binding energy demonstrates the binding of holes for small U/t, resulting from the interplay between U and V. Superconductivity arises in a limited window of V depending on U. However, the effective dominance of either U or V results in the annihilation of these hole pairs. The presence of two peaks in specific heat is caused by two Coulomb interactions. The development of doublons as V increases leads to a more ordered state, lowering entropy. The thermodynamic properties also show that the t−J−U−V model acts as an attractive Hubbard model for U<V. However, a pure attractive t−J−U model cannot explain these phenomenologies.

Gaussian variational method to Fermi-Hubbard model in one and two dimensions

The study of ground-state properties of the Fermi-Hubbard model is a long-lasting task in the research of strongly correlated systems, and is crucial for the understanding of notable quantum phenomena including superconductivity and magnetism. Owing to the exponentially growing complexity of the system, a quantitative analysis usually demands high computational cost and is restricted to small samples, especially in two or higher dimensions. Here, we introduce a variational method in the frame of fermionic Gaussian states, and obtain the ground states of one- and two-dimensional attractive Hubbard models via imaginary-time evolution. We calculate the total energy and benchmark the results in a wide range of interaction strength and filling factor with those obtained via exact two-body results, the density matrix renormalization group based on matrix product states (MPS), and projector Quantum Monte Carlo (QMC) method. For both 1D and 2D cases, the Gaussian variational method presents accurate results for total energy with a maximum systematic error in the intermediate interaction region. The accuracy of these results has negligible dependence on the system size. We further calculate the double occupancy and find excellent agreement with MPS and QMC, as well as the experimental results of cold quantum gases in optical lattices. The results suggest that the Gaussian pairing state is a good approximation to the ground states of attractive Hubbard model, in particular in the strong and weak coupling limits. Moreover, we generalize the method to the attractive Hubbard model with a finite spin-polarization, which can be mapped to the repulsive interaction case via particle-hole transformation, and obtain accurate results of ground state energy and double occupancy. Our work demonstrates the ability of the Gaussian variational method to extract ground state properties of strongly correlated many-body systems with negligible computational cost, especially of large size and in higher dimensions.

Spin-singlet topological superconductivity in the attractive Rashba-Hubbard model

Fully gapped, spin-singlet superconductors with antisymmetric spin-orbit coupling in a Zeeman magnetic field provide a promising route to realize superconducting states with non-Abelian topological order and therefore fault-tolerant quantum computation. Here we use a quantum Monte Carlo dynamical cluster approximation to study the superconducting properties of a doped two-dimensional attractive Hubbard model with Rashba spin-orbit coupling in a Zeeman magnetic field. We generally find that the Rashba coupling has a beneficial effect towards $s$-wave superconductivity. In the presence of a finite Zeeman field, when superconductivity is suppressed by Pauli pair breaking, the Rashba coupling counteracts the spin imbalance created by the Zeeman field by mixing the spins, and thus restores superconductivity at finite temperatures. We show that this favorable effect of the spin-orbit coupling is traced to a spin-flip driven enhancement of the amplitude for the propagation of a pair of electrons in time-reversed states. Moreover, by inspecting the Fermi surface of the interacting model, we show that for sufficiently large Rashba coupling and Zeeman field, the superconducting state is expected to be topologically nontrivial.

η -pairing on square and triangular lattices

The $\ensuremath{\eta}$-pairing is a type of Cooper pairing state in which the phase of the superconducting order parameter is aligned in a staggered manner, in contrast to the usual BCS superconductors with a spatially uniform phase. In this study, we search for a characteristic $\ensuremath{\eta}$-pairing state in a triangular lattice where a simple staggered alignment of the phase is not possible. As an example, we consider the attractive Hubbard model on both the square and triangular lattices under a strong external Zeeman field. Using the mean-field approximation, we have identified several $\ensuremath{\eta}$-pairing states. Additionally, we have examined the electromagnetic stability of the pairing state by calculating the Meissner kernel. Odd-frequency pairing plays a crucial role in achieving a diamagnetic response if the electrons experience a staggered superconducting phase during the propagation of current.

Local density of states fluctuations in a two-dimensional superconductor as a probe of quantum diffusion

The interplay of superconductivity and disorder generates a wealth of complex phenomena. In particular, the peculiar structure of diffusive electronic wavefunctions is predicted to increase the superconducting critical temperature in some range of disorder. In this work, we use an epitaxial monolayer of lead showing a simple band structure and homogenous structural disorder as a model system of a 2D superconductor in the weak-antilocalization regime. Then, we perform an extensive study of the emergent fluctuations of local density of states (LDOS) and spectral energy gap in this material and compare them with both analytical results and numerical solution of the attractive Hubbard model. We show that mesoscopic LDOS fluctuations allow to probe locally both the elastic and inelastic scattering rates which are notoriously difficult to measure in transport measurements.

Quantum Monte Carlo study of the attractive kagome-lattice Hubbard model

Quantum Monte Carlo study of the attractive kagome-lattice Hubbard model

Proximity-induced charge density wave in a metallic system

Non-local quasiparticles in correlated quantum materials can exhibit the proximity effect. For instance, in metal superconductor hybrid systems, the leaking of cooper pairs to the metallic region induces superconducting correlations in a standard metal. This paper explores the proximity effects of charge density wave (CDW) on metal using the attractive Hubbard model, which harbors CDW state at half-filling. Our fully self-consistent calculations demonstrate that periodic charge modulations develop in a metal due to the tunneling of finite momentum particle-hole pairs from the CDW region. Upon doping the normal region, the commensurate CDW changes to an incommensurate one by incorporating regular phase shifts. Furthermore, the induced CDW produces a soft gap in the density of states and thus can be detected in tunneling experiments. We discuss our results in light of recent reports of such proximity-induced charge order in different two-dimensional heterostructures.

Supercurrent Distribution on Ammann-Beenker Structure

We study the distribution of supercurrent in the attractive Hubbard model on a periodic approximant of the Ammann-Beenker structure by means of the Bogoliubov-de Gennes (BdG) mean-field theory. We first investigate the spatial distributions of the electron density and superconducting order parameter and find a crossover between superconducting states with (i) extended, (ii) localized, and (iii) short-ranged Cooper pairs, similar to the previous results on the Penrose tiling. Furthermore, we formulate the expression of the supercurrent for the periodic approximant in terms of the eigenenergies and the wave functions of the Bogoliubov-de Gennes Hamiltonian and numerically investigate how the local supercurrent distribution varies by changing the direction of the applied phase gradient.

Second-Neighbor Hopping Effects in the Two-Dimensional Attractive Hubbard Model

The emergence of superconductivity (SC) in lattice models, such as the attractive Hubbard one, has renewed interest since the realization of cold-atom experiments. However, reducing the temperature in these experiments is a bottleneck; therefore, investigating how to increase the energy scale for SC is crucial to cold atoms. In view of this, we examine the effects of next-nearest-neighbor hoppings (t′) on the pairing properties of the attractive Hubbard model in a square lattice. To this end, we analyze the model through unbiased Quantum Monte Carlo simulations for fixed density n=0.87, and perform finite-size scaling analysis to the thermodynamic limit. As our main result, we notice that the existence of further hopping channels leads to an enhancement of the pairing correlations, which, in turn, increases the ground-state order parameter Δ. Finally, at finite temperatures, for t′/t≠0, this enhancement of pairing correlations leads to an increase in the critical temperature Tc. That is, the fine-tuning of second-neighbor hoppings increases the energy scales for SC, and may be a route by which cold-atom experiments can achieve such a phase and to help us further understand the nature of this phenomenon.

Density-matrix functional theory of the attractive Hubbard model: Statistical analogy of pairing correlations

The ground-state properties of the Hubbard model with attractive local pairing interactions are investigated in the framework of lattice density-functional theory. A remarkable correlation is revealed between the interaction-energy functional $W[\mathbit{\ensuremath{\eta}}]$ corresponding to the Bloch-state occupation-number distribution ${\ensuremath{\eta}}_{\ensuremath{\kappa}\ensuremath{\sigma}}$ and the entropy $S[\mathbit{\ensuremath{\eta}}]$ of a system of noninteracting fermions having the same ${\ensuremath{\eta}}_{\mathbit{k}\ensuremath{\sigma}}$. The relation between $W[\mathbit{\ensuremath{\eta}}]$ and $S[\mathbit{\ensuremath{\eta}}]$ is shown to be approximately linear for a wide range of ground-state representable occupation-number distributions ${\ensuremath{\eta}}_{\mathbit{k}\ensuremath{\sigma}}$. Taking advantage of this statistical analogy, a simple explicit ansatz for $W[\mathbit{\ensuremath{\eta}}]$ of the attractive Hubbard model is proposed, which can be applied to arbitrary periodic systems. The accuracy of this approximation is demonstrated by calculating the main ground-state properties of the model on several 1D and 2D bipartite and nonbipartite lattices and by comparing the results with exact diagonalizations.

Charge excitations across a superconductor-insulator transition

We study the superconductor-insulator transition (SIT) in the ground state of the attractive honeycomb Hubbard model in the presence of a staggered potential (a mass term), using a combination of unbiased computational methods, namely, exact diagonalization and quantum Monte Carlo simulations. We probe the nature of the lowest-energy charge excitations across the SIT and show that they are bosonic, as inferred (and shown in the strongly interacting regime) in a previous study of the same model in the square lattice. Increasing the strength of the staggered potential leads to a crossover in which bosonic low-energy excitations give way to fermionic ones within the insulating phase. We also show that the SIT belongs to the $3d$-XY universality class, like in its square lattice counterpart. The robustness of our results in these two lattice geometries supports the expectation that our findings are universal for SITs in clean systems.

Disorder stabilized breached-pair phase in an s -wave superconductor

The breached-pair state wherein superconductivity coexists with magnetic polarization is known to exist as a ground state of an imbalanced Fermi system only under very fine-tuned conditions. Here, we show that an s-wave superconductor that is well described by a spin-selectively disordered attractive Hubbard model away from half filling has the breached-pair state as a ground-state without the need for such fine-tuning. The existence of this breached-pair phase is established by laying recourse to a Monte Carlo technique called static path approximation (SPA). Further, by using the SPA, we map out the entire phase diagram of the spin-selectively disordered attractive Hubbard model and show that apart from the breached-pair phase, the many-body system hosts the putative s-wave superconducting state and a polarized Fermi-liquid state.

Superconductivity enhanced by pair fluctuations between wide and narrow bands

Full or empty narrow bands near the Fermi level are known to enhance superconductivity by promoting scattering processes and spin fluctuations. Here, we demonstrate that doublon-holon fluctuations in systems with half-filled narrow bands can similarly boost the superconducting ${T}_{c}$. We study the half-filled attractive bilayer Hubbard model on the square lattice using dynamical mean-field theory. The band structure of the noninteracting system contains a wide band formed by bonding orbitals and a narrow band formed by antibonding orbitals, with bandwidths tunable by the interlayer hopping. The shrinking of the narrow band can lead to a substantial increase in the superconducting order parameter and phase stiffness in the wide band. At the same time, the coupling to the wide band allows the narrow band to remain superconducting---and to reach the largest order parameter---in the flat band limit. We develop an anomalous worm sampling method to study superconductivity in the limit of vanishing effective hopping. By analyzing the histogram of the local eigenstates, we clarify how the interplay between different interaction terms in the bonding/antibonding basis promotes pair fluctuations and superconductivity.

Finite-temperature study of correlations in a bilayer band insulator

We perform the finite-temperature determinant quantum Monte Carlo simulation for the attractive Hubbard model on the half-filled bilayer square lattice. Recent progress on optical lattice experiments lead us to investigate various single-particle properties such as momentum distribution and double occupancies which should be easily measured in cold-atom experiments. The pair-pair and the density-density correlations have been studied in detail, and through finite-size scaling, we show that there is no competing charge density wave order in the bilayer band-insulator model and that the superfluid phase is the stable phase for the interaction range $\abs{U}/t = 5-10$. We show the existence of two energy scales in the system as we increase the attractive interaction, one governing the phase coherence and the other one corresponding to the molecule formation. In the end, we map out the full $T-U$ phase diagram and compare the $T_c$ obtained through the mean-field analysis. We observe that the maximum $T_c/t(= 0.27)$ occurs for $\abs{U}/t = 6$, which is roughly twice the reported $T_c$ of the single-layer attractive Hubbard model.

Subgap two-particle spectral weight in disordered s -wave superconductors: Insights from mode coupling approach

We study the two-particle spectral functions and collective modes of weakly disordered superconductors using a disordered attractive Hubbard model on a square lattice. We show that the disorder-induced scattering between collective modes leads to a finite subgap spectral weight in the long-wavelength limit. In general, the spectral weight is distributed between the phase and the Higgs channels, but as we move towards half filling the Higgs contribution dominates. The inclusion of the density fluctuations lowers the frequency at which this mode occurs and results in the phase channel gaining a larger contribution to this subgap mode. Near half filling, the proximity of the system to the charge density wave instability leads to strong fluctuations of the effective disorder at the commensurate wave vector ($[\ensuremath{\pi},\ensuremath{\pi}]$). We develop an analytical mode coupling approach where the pure Goldstone mode in the long-wavelength limit couples to the collective mode at $[\ensuremath{\pi},\ensuremath{\pi}]$. This provides insight into the location and distribution of the two-particle spectral weights between the Higgs and the phase channels.