On-site Attraction Research Articles

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.

Superconductivity, Charge Density Wave, and Supersolidity in Flat Bands with a Tunable Quantum Metric.

Predicting the fate of an interacting system in the limit where the electronic bandwidth is quenched is often highly nontrivial. The complex interplay between interactions and quantum fluctuations driven by the band geometry can drive competition between various ground states, such as charge density wave order and superconductivity. In this work, we study an electronic model of topologically trivial flat bands with a continuously tunable Fubini-Study metric in the presence of on-site attraction and nearest-neighbor repulsion, using numerically exact quantum MonteCarlo simulations. By varying the electron filling and the minimal spatial extent of the localized flat-band Wannier wave functions, we obtain a number of intertwined orders. These include a phase with coexisting charge density wave order and superconductivity, i.e., a supersolid. In spite of the nonperturbative nature of the problem, we identify an analytically tractable limit associated with a "small" spatial extent of the Wannier functions and derive a low-energy effective Hamiltonian that can well describe our numerical results. We also provide unambiguous evidence for the violation of any putative lower bound on the zero-temperature superfluid stiffness in geometrically nontrivial flat bands.

Connection between the semiconductor-superconductor transition and the spin-polarized superconducting phase in the honeycomb lattice

The band structure of noninteracting fermions in the honeycomb lattice exhibits the Dirac cones at the corners of the Brillouin zone. As a consequence, fermions in this lattice manifest a semiconducting behavior below some critical value of the onsite attraction, $U_{c}$. However, above $U_{c}$, the superconducting phase can occur. We discuss an interplay between the semiconductor--superconductor transition and the possibility of realization of the spin-polarized superconductivity (the so-called Sarma phase). We show that the critical interaction can be tuned by the next-nearest-neighbor (NNN) hopping in the absence of the magnetic field. Moreover, a critical value of the NNN hopping exists, defining a range of parameters for which the semiconducting phase can emerge. In the weak coupling limit case, this quantum phase transition occurs for the absolute value of the NNN hopping equal to one third of the hopping between the nearest neighbors. Similarly, in the presence of the magnetic field, the Sarma phase can appear, but only in a range of parameters for which initially the semiconducting state is observed. Both of these aspects are attributed to the Lifshitz transition, which is induced by the NNN hopping as well as the external magnetic field.

Three-body problem in a multiband Hubbard model

We consider the three-body problem in a generic multiband lattice, and analyze the dispersion of the trimer states that are made of two spin-$\uparrow$ fermions and a spin-$\downarrow$ fermion due to an onsite attraction in between. Based on a variational approach, we first obtain the exact solution in the form of a set of coupled integral equations, and then reduce it to an eigenvalue problem. As an illustration we apply our theory to the sawtooth lattice, and numerically show that energetically-stable trimers are allowed in a two-band setting, which is in sharp contrast with the single-band linear-chain model. In particular we also reveal that the trimers have a nearly-flat dispersion when formed in a flat band, which is unlike the highly-dispersive spectrum of its dimers.

Effective-mass tensor of the two-body bound states and the quantum-metric tensor of the underlying Bloch states in multiband lattices

By considering an on-site attraction between a spin-$\ensuremath{\uparrow}$ and a spin-$\ensuremath{\downarrow}$ fermion in a multiband tight-binding lattice, here we study the two-body spectrum and derive an exact relation between the inverse of the effective-mass tensor of the lowest bound states and the quantum-metric tensor of the underlying Bloch states. In addition to the intraband (or the so-called conventional) contribution that depends only on the single-particle spectrum and the interband (or the so-called geometric) contribution that is controlled by the quantum metric, our generalized relation has an additional interband contribution that depends on the so-called band-resolved quantum metric. All of our analytical expressions are applicable to those multiband lattices that simultaneously exhibit time-reversal symmetry and fulfill the condition on spatially uniform pairing. As a nontrivial illustration we analyze the two-body problem in a kagome lattice with nearest-neighbor hoppings, and we show that the exact relation provides a perfect benchmark.

Superconducting and normal properties of the low-dimensional phases of the metallic hydrogen

In the first part of the paper we consider properties of a two-dimensional low density (n = 1) electron system with strong onsite Hubbard attraction U >W (W is the bandwidth) in the presence of a strong random potential V uniformly distributed in the range from -V to +V. In the framework of the Bogoliubov-de Gennes approach we observed an appearance of inhomogeneous state of spatially separated Fermi-Bose mixture of Cooper pairs and unpaired electrons with the formation of bosonic droplets of different size in the unpaired fermionic matrix. Software package to solve the system of Eliashberg equations that describes the transition of a metal to a superconducting state is presented. We use a version of the Eliashberg system of equations written on the imaginary axis. The system is presented in two versions: without taking into account the corrections for the chemical potential of electrons and with taking them into account. The calculations were performed for the I41/amd phase of metallic hydrogen at a pressure of 500 GPa.

Optical spectral weight, phase stiffness, and Tc bounds for trivial and topological flat band superconductors

We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat-band superconductors that lead to upper bounds for the superfluid stiffness and the two-dimensional (2D) [Formula: see text] We focus on on-site attraction [Formula: see text] on the Lieb lattice with trivial flat bands and on the π-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weight [Formula: see text] with [Formula: see text] , where n is the flat-band density and Ω is the Marzari-Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound for [Formula: see text] linear in [Formula: see text] We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results.

Pairing and Pair Superfluid Density in One-Dimensional Two-Species Fermionic and Bosonic Hubbard Models.

We use unbiased computational methods to elucidate the onset and properties of pair superfluidity in two-species fermionic and bosonic systems with onsite interspecies attraction loaded in a uniform, i.e., with no confining potential, one-dimensional optical lattice. We compare results from quantum MonteCarlo (QMC) and density matrix renormalization group (DMRG), emphasizing the one-to-one correspondence between the Drude weight tensor, calculated with DMRG, and the various winding numbers extracted from the QMC. Our results show that, for any nonvanishing attractive interaction, pairs form and are the sole contributors to superfluidity; there are no individual contributions due to the separate species. For weak attraction, the pair size diverges exponentially, i.e., Bardeen-Cooper-Schrieffer (BCS) pairing, requiring huge systems to bring out the pair-only nature of the superfluid. This crucial property is largely overlooked in many studies, thereby misinterpreting the origin and nature of the superfluid. We compare and contrast this with the repulsive case and show that the behavior is very different, contradicting previous claims about drag superfluidity and the symmetry of properties for attractive and repulsive interactions. Finally, our results show that the situation is similar for soft-core bosons: superfluidity is due only to pairs, even for the smallest attractive interaction strength compatible with the largest system sizes that we could attain.

Droplets of the Order Parameter in a Low Density Attracting Electron System in the Presence of a Strong Random Potential

The properties of a two-dimensional low density (n<<1) electron system with strong onsite Hubbard attraction U>W (W is the bandwidth) in the presence of a strong random potential V uniformly distributed in the range from -V to +V are considered. Electronic hoppings only at neighboring sites on the square lattice are taken into account, thus W=8t. The calculations were carried out for a lattice of 24x24 sites with periodic boundary conditions. In the framework of the Bogoliubov - de Gennes approach we observed an appearance of inhomogeneous states of spatially separated Fermi-Bose mixture of Cooper pairs and unpaired electrons with the formation of bosonic droplets of different size in the matrix of the unpaired normal states We observed a decrease in the droplet size (from larger droplets to individual bielectronic pairs) when we decrease the electron density at fixed values of the Hubbard attraction and random potential. The obtained results are important for the construction of the gross phase diagram and understanding of the nature of the phase transition between superconducting, normal metallic and localized states in quasi-2D (thin) film of a dirty metal. In a more practical sense it is interesting also for the experimental implementation of superconducting qubits on quantum circuits with high impedances in granular superconductors.

The influence of strong diagonal disorder on superconductivity in the 2D attractive-U Hubbard model at low electron density

The properties of a two-dimensional low density (n<<1) electron system with strong onsite Hubbard attraction U>W (W is the bandwidth) in the presence of a strong random potential V uniformly distributed in the range from -V to +V are considered. Electronic hoppings only at neighboring sites on the square lattice are taken into account, thus W=8t. The calculations were carried out for a lattice of 24x24 sites with periodic boundary conditions. In the framework of the Bogoliubov - de Gennes approach we observed an appearance of inhomogeneous state of spatially separated Fermi-Bose mixture of Cooper pairs and unpaired electrons with the formation of bosonic droplets of different size in the unpaired fermionic matrix. We observed an increase in the droplet size (from individual bielectronic pairs to larger droplets and finally to the percolation cluster) when we increase the electron density at fixed values of the Hubbard attraction and random potential.

Interplay between local response and vertex divergences in many-fermion systems with on-site attraction

We investigate the divergences appearing in the two-particle irreducible vertex functions of many-fermion systems with attractive on-site interactions. By means of dynamical mean-field theory calculations, we determine the location of singularity lines in the phase diagram of the attractive Hubbard model at half-filling, where the local Bethe-Salpeter equations are non invertible. We find that divergences appear both in the magnetic and in the density scattering channels. The former affect a sector of suppressed fluctuations and comply with the mapping of the physical susceptibilities of the repulsive case. At the same time, the appearance of singularities in the density channel of the attractive model demonstrates that vertex divergences can also plague the dominant scattering sectors associated with enhanced local susceptibilities. This constitutes a counterexample to previously proposed interpretations. Eventually, by exploiting the underlying physical symmetries and a spectral representation of the susceptibilities, we clarify the relation between vertex divergences and the local response of the system in different channels.

Topological superconductivity in Dirac honeycomb systems

We predict two topological superconducting phases in microscopic models arising from the Berry phase associated with the valley degree of freedom in gapped Dirac honeycomb systems. The first one is a topological helical spin-triplet superconductor with a nonzero center-of-mass momentum that does not break time-reversal symmetry. We also find a topological chiral-triplet superconductor with Chern number $\pm 1$ with equal-spin-pairing in one valley and opposite-spin-triplet pairing in the other valley. Our results are obtained for the Kane-Mele model in which we have explored the effect of three different interactions, onsite attraction $U$, nearest-neighbor density-density attraction $V$, and nearest-neighbor antiferromagnetic exchange $J$, within self-consistent Bogoliubov--de Gennes theory. Transition metal dichalcogenides and cold atom experiments are promising platforms to explore these phases.

Charge Order of Strongly Bounded Electron Pairs on the Triangular Lattice: the Zero-Bandwidth Limit of the Extended Hubbard Model with Strong Onsite Attraction

The inhomogeneous distribution of charged particles is known as charge-order phenomena. Recent experimental studies of (quasi-) two-dimensional materials found different ordered patterns on the triangular lattice. In this work, the preliminary studies of the extended Hubbard model (with the intersite Coulomb density-density repulsion) in the atomic limit on the triangular lattice are presented. The model is investigated within the mean-field approach that treats the onsite term exactly. The finite temperature phase diagrams including metastable phases and some characteristics of the model are determined for the limit of strong onsite attraction. It is shown that in the limit considered all transitions between stable phases are discontinuous (for fixed chemical potential), which is totally different from the model on the alternate lattices. Continuous transitions between metastable phases are also found.

Repulsion-attraction asymmetry in the Bose-Fermi-Hubbard model

It is shown that in the Bose-Fermi-Hubbard model, used for a description of the atomic boson-fermion mixture in the optical lattice, the fermion-hole symmetry allows one to establish a correspondence between cases of the on-site repulsion and attraction. Based on the phase diagrams, built with the help of a corresponding transformation of model parameters within the framework of the grand canonical ensemble, the conditions of the superfluid phase existence at the boson-fermion attraction are analyzed. The phase diagrams that illustrate the difference of behavior of the BF mixture in the cases of BF repulsion or attraction are obtained. A relation to the available experimental data is discussed.

Mapping repulsive to attractive interaction in driven–dissipative quantum systems

Repulsive and attractive interactions usually lead to very different physics. Striking exceptions exist in the dynamics of driven–dissipative quantum systems. For the example of a photonic Bose–Hubbard dimer, we establish a one-to-one mapping relating cases of onsite repulsion and attraction. We prove that the mapping is valid for an entire class of Markovian open quantum systems with a time-reversal-invariant Hamiltonian and physically meaningful inverse-sign Hamiltonian. To underline the broad applicability of the mapping, we illustrate the one-to-one correspondence between the nonequilibrium dynamics in a geometrically frustrated spin lattice and those in a non-frustrated partner lattice.

Unconventional spin-charge phase separation in a model 2D cuprate

In this work, we address a challenging problem of a competition of charge and spin orders for high-T c cuprates within a simplified 2D spin-pseudospin model which takes into account both conventional Heisenberg Cu2+−Cu2+ antiferromagnetic spin exchange coupling (J) and the on-site (U) and intersite (V) charge correlations in the CuO2 planes with the on-site Hilbert space reduced to only three effective charge states (nominally Cu1+;2+;3+). We performed classical Monte Carlo calculations for large square lattices implying the mobile doped charges and focusing on a case of a small intersite repulsion V ≪ J. The on-site attraction (U 0) the homogeneous ground state antiferromagnetic solutions of the doped system found in a mean-field approximation are shown to be unstable with respect to a phase separation with the charge and spin subsystems behaving like immiscible quantum liquids. Puzzlingly, with lowering the temperature one can observe two sequential phase transitions: first, an antiferromagnetic ordering in the spin subsystem diluted by randomly distributed charges, then, a charge condensation in the charge droplets. The effects are illustrated by the Monte Carlo calculations of the specific heat and longitudinal magnetic susceptibility.

Various Charge-Ordered States in the Extended Hubbard Model with On-Site Attraction in the Zero-Bandwidth Limit

The extended Hubbard model in the zero-bandwidth limit with intersite density–density interactions (nearest- and next-nearest-neighbor) is analyzed in the site-dependent mean-field approximation. In this paper, we investigate a case of on-site attraction U<0 for arbitrary values of intersite interactions as well as chemical potential (or electron density). We present ground state and finite temperature phase diagrams obtained in the four-sublattice assumption (e.g., 1D chain, 2D square, or 3D body-centered cubic lattices). Our results for U<0 show that in the system various phases emerge: three different types of charge-ordered phases (checkerboard, laminar/stripe, and four-subllatice-type) and non-ordered phases.

Orbital order from the on-site orbital attraction

We study the model of Fe-based superconductors with intraorbital attraction, designed to favor a spontaneous orbital polarization. Previous studies of this model within the two-orbital approximation indicated that the leading instability is toward s-wave superconductivity and the subleading one is toward anti-ferro-orbital order, which breaks the translational symmetry of the crystal. The two-orbital approximation is, however, not consistent with the Fermi surface geometry of Fe superconductors, as it yields the wrong position of one of the hole pockets. Here we analyze the model with the same interaction but with realistic Fermi surface geometry (two hole pockets at the center of the Brillouin zone and two electron pockets at its boundary). We apply the parquet renormalization-group (pRG) technique to detect the leading instability upon the lowering of the temperature. We argue that the pRG analysis strongly favors a q = 0 orbital order, which in the band basis is a d-wave Pomeranchuk order.

Quantum Correlations of Few Dipolar Bosons in a Double-Well Trap

We consider $N$ interacting dipolar bosonic atoms at zero temperature in a double-well potential. This system is described by the two-space-mode extended Bose-Hubbard (EBH) Hamiltonian which includes (in addition to the familiar BH terms) the nearest-neighbor interaction, correlated hopping and bosonic-pair hopping. For systems with $N=2$ and $N=3$ particles we calculate analytically both the ground state and the Fisher information, the coherence visibility, and the entanglement entropy that characterize the correlations of the lowest energy state. The structure of the ground state crucially depends on the correlated hopping $K_c$. On one hand we find that this process makes possible the occurrence of Schr\"odinger-cat states even if the onsite interatomic attraction is not strong enough to guarantee the formation of such states. On the other hand, in the presence of a strong onsite attraction, sufficiently large values of $|K_c|$ destroys the cat-like state in favor of a delocalized atomic coherent state.

Fermion quartets in a two-band model of superconductivity

A two-band superconducting fermion system is investigated. Apart from an on-site two-fermion attraction acting in the wider band an on-site four-fermion attraction is introduced. The four-fermion potential binds four electrons from both of the bands residing on a lattice site into a fermion quartet. Additionally, the local Coulomb repulsion is involved in the narrower band. There exist two order parameters in the system: a conventional BCS-type gap and a quartet one. The ground state properties such as the dependence of these order parameters on the Coulomb repulsion and the four-fermion attraction are examined. Furthermore, the average numbers of electrons constituting the system as functions of the interactions are displayed as well. It is shown that quartet superconductivity is very sensitive to the Coulomb repulsion and when subject to this interaction quartets disappear for quite small values of that. Finally, the response to an external magnetic field is studied. This reveals a quite complicated behavior of the system because in general two electric currents can flow through a specimen but there exist conditions under which one of them disappears. Such a behavior is determined by the dependence of both currents on the strength of the Coulomb repulsion and the four-fermion attraction. Two scenarios with dx2-y2-wave pairing are investigated on an initial stage as well.