Attractive On-site Interaction Research Articles

Fragility of the Schrödinger Cat in thermal environments

We describe the decoherence instability of Schrödinger Cat states in the two-site Bose-Hubbard model with an attractive on-site interaction between particles. For N particles with onsite attractive energy U and hopping amplitude between sites t, Cat states exist for uequiv frac{UN}{2t}<-1 at zero temperature. However, they are increasingly unstable to small thermal fluctuations as the Cat itself is increasingly well-defined and its components become well-separated. For any given u<-1, the decoherence temperature becomes smaller for large N. The loss of off-diagonal coherence peaks in the equilibrium density matrix is dominated by the thermal admixture of the first excited state of the many-body system with its ground state. Particle number fluctuations, described in the grand canonical ensemble also reduce coherence, but to a lesser degree than thermal fluctuations. The full density matrix of the Schrödinger Cat is obtained by exact numerical diagonalization of the many-body Hamiltonian and a narrow regime in the parameter space of the particle number, temperature, and U/t is identified where small Cat states may survive decoherence in a physical environment.

Magnetocaloric and electrocaloric heat engine and refrigeration cycles in the open Fermi-Hubbard optical dimer with attractive interactions

Quantum heat engines and refrigerators can be realized in a Fermi-Hubbard optical dimer through immersion in a mean-field Fermi gas bath using the magnetocaloric and electrocaloric effects. It is demonstrated that in the presence of onsite and heat bath-induced attractive interactions, singlet-to-triplet transitions are achieved with a finite external magnetic field. Similarly, triplet-to-singlet transitions occur in the presence of an applied finite electric field. Results show that to lift the degeneracies, considerable electric potential magnitudes are needed. These magnitudes are greater than the magnetic potential strengths where the degeneracies occur. Furthermore, in the attractive regime, combinations of direct and inverse caloric effects can be combined to operate quantum heat engines and refrigerators, like what happens in the repulsive regime.

Topological two-body bands in a multiband Hubbard model

In a multiband Hubbard model the self-consistency relations for the two-body bound-state bands are in the form of a nonlinear eigenvalue problem. Assuming that the resultant eigenvectors form an orthonormal set, e.g., in the strong-binding regime, here we reformulate their Berry curvatures and the associated Chern numbers. As an illustration we solve the two-body problem in a Haldane-Hubbard model with attractive on-site interactions and analyze its topological phase diagrams from weak to strong couplings, i.e., by keeping track of the gap closings in between the low-lying two-body bands. The resultant Chern numbers are consistent with the lobe structure of the phase diagrams in the strong-coupling regime.

Exploring interacting topological insulator in the extended Su-Schrieffer-Heeger model

Exploring topological phases in interacting systems is a challenging task. We investigate many-body topological physics of interacting fermions in an extended Su-Schrieffer-Heeger (SSH) model, which extends the two sublattices of SSH model into four sublattices and thus is dubbed SSH4 model, based on the density-matrix renormalization-group numerical method. The interaction-driven phase transition from topological insulator to charge density wave (CDW) phase can be identified by analyzing the variations of entanglement spectrum, entanglement entropies, energy gaps, CDW order parameter, and fidelity. We map the global phase diagram of the many-body ground state, which contains nontrivial topological insulator, trivial insulator and CDW phases, respectively. In contrast to interacting SSH model, in which the phase transitions to the CDW phase are argued to be first-order phase transitions, the phase transitions between the CDW phase and topologically trivial/nontrivial phases are shown to be continuous phase transitions. Finally, we {also} show the phase diagram of interacting spinful SSH4 model, where the attractive (repulsive) on-site spin interaction amplifies (suppresses) the CDW phase. The models analyzed here can be implemented with ultracold atoms on optical superlattices.

Superconductivity of non-Fermi liquids described by Sachdev-Ye-Kitaev models

We investigate models of electrons in the Sachdev-Ye-Kitaev class with random and all-to-all electron hopping, electron spin exchange, and Cooper-pair hopping. An attractive on-site interaction between electrons leads to superconductivity at low temperatures. Depending on the relative strengths of the hopping and spin exchange, the normal state at the critical temperature is either a Fermi-liquid or a non-Fermi liquid. We present a large-$M$ (where spin symmetry is enlarged to SU$(M)$) study of the normal state to superconductor phase transition. We describe the transition temperature, the superconducting order parameter, and the electron spectral functions. We contrast between Fermi liquid and non-Fermi liquid normal states: we find that for weaker attractive on-site interaction there is a relative enhancement of $T_c$ when the normal state is a non-Fermi liquid, and correspondingly a strong deviation from BCS limit. Also, the phase transition in this case becomes a first-order transition for strong non-Fermi liquids. On the other hand, for stronger on-site interaction, there is no appreciable difference in $T_c$ between whether the superconductivity emerges from a Fermi liquid or a non-Fermi liquid. Notable features of superconductivity emerging from a non-Fermi liquid are that the superconducting electron spectral function is different from the Fermi-liquid case, with additional peaks at higher energies, and there is no Hebel-Slichter peak in the NMR relaxation rate in the non-Fermi liquid case.

Dimers, trimers, tetramers, and other multimers in a multiband Bose-Hubbard model

We study the bound states of $N$ identical bosons that are described by a multiband Bose-Hubbard model with generic hoppings and an attractive onsite interaction. Using a variational approach, we first derive exact integral equations for the dimers, trimers, tetramers, and other multimers, and then apply them to a one-dimensional sawtooth model that features two bands. In particular we reveal the presence of not only the offsite dimer states which consist of two monomers on different sites even in the strong-coupling limit but also the offsite trimer states which consist of either a dimer on one site and a monomer on another site or three monomers on three different sites. Our variational calculations for the ground states of onsite dimers, onsite trimers and offsite trimers benchmark perfectly well with the DMRG simulations. We also present DMRG results for the ground states of onsite tetramers, offsite tetramers, onsite pentamers, offsite pentamers, and for those of other multimers.

Stability of (N+1) -body fermion clusters in a multiband Hubbard model

We start with a variational approach and derive a set of coupled integral equations for the bound states of $N$ identical spin-$\ensuremath{\uparrow}$ fermions and a single spin-$\ensuremath{\downarrow}$ fermion in a generic multiband Hubbard Hamiltonian with an attractive on-site interaction. As an illustration, we apply our integral equations to the one-dimensional sawtooth lattice up to $N\ensuremath{\le}3$, i.e., to the $(3+1)$-body problem, and we reveal not only the presence of tetramer states in this two-band model but also their quasiflat dispersion when formed in a flat band. Furthermore, for $N={4,5,\ensuremath{\cdots},10}$, our density-matrix renormalization-group simulations and exact diagonalization suggest the presence of larger and larger multimers with lower and lower binding energies, conceivably without an upper bound on $N$. These peculiar $(N+1)$-body clusters are in sharp contrast with the exact results on the single-band linear-chain model where none of the $N\ensuremath{\ge}2$ multimers appear. Hence their presence must be taken into account for a proper description of the many-body phenomena in flat-band systems, e.g., they may suppress superconductivity especially when there exists a large spin imbalance.

Revisiting Anderson-Higgs mechanism: application of Lieb-Schultz-Mattis theorem

We consider an electron model of superconductivity on a three-dimensional lattice where there are on-site attractive Hubbard interaction and long-range repulsive Coulomb interaction. It is claimed that fully gapped s-wave superconductivity within this model, if present, exhibits spontaneous translation symmetry breaking possibly related to a charge order. Our discussions are based on an application of the Lieb-Schultz-Mattis theorem under some physical assumptions. The inconsistency between the proposed supersolid and experiments can impose some constraints on a reasonable choice of a theoretical model.

Enhancement of pairing correlations due to nearly flat bands in the plaquette-Lieb Hubbard model

Motivated by recent research works on the flat-band correlated electron systems, we construct a plaquette-Lieb lattice, which exhibits nearly flat bands close to the Fermi level around half-filling, when the inter-plaquette hopping integral is much smaller than the intra-plaquette one. A detailed comparison study with the well-known checkerboard lattice indicates that there exist significant differences for the pairing property between the two lattices, and the nearly flat bands on the plaquette-Lieb lattice strongly enhance the [Formula: see text]-wave pairing correlation for repulsive on-site Hubbard interaction and [Formula: see text]-wave pairing correlation for attractive on-site Hubbard interaction. Our study not only provides a new lattice with nearly flat bands, but also deepens the understanding of electronic structure on superconductivity.

Signatures of the BCS-BEC crossover in the yrast spectra of Fermi quantum rings

We study properties of the lowest energy states at non-zero total momentum (yrast states) of the Hubbard model for spin-1/2 fermions in the quantum ring configuration with attractive on-site interaction at low density. In the one-dimensional (1D) case we solve the Hubbard model using the Bethe ansatz, while for the crossover into the 2D regime we use the Full-Configuration-Interaction Quantum Monte-Carlo method (FCIQMC) to obtain the yrast states for the spin-balanced Fermi system. We show how the yrast excitation spectrum changes from the 1D to the 2D regime and how pairing affects the yrast spectra. We also find signatures of fragmented condensation for certain yrast states usually associated with dark solitons.

Flat-band superconductivity for tight-binding electrons on a square-octagon lattice

The discovery of superconductivity in twisted bilayer graphene has triggered a resurgence of interest in flat-band superconductivity. Here, we investigate the square-octagon lattice, which also exhibits two perfectly flat bands when next-nearest neighbour hopping or an external magnetic field are added to the system. We calculate the superconducting phase diagram in the presence of on-site attractive interactions and find two superconducting domes, as observed in several types of unconventional superconductors. The critical temperature shows a linear dependence on the coupling constant, suggesting that superconductivity might reach high temperatures in the square-octagon lattice. Our model could be experimentally realized using photonic or ultracold atoms lattices.

Quantum walks of interacting Mott-insulator defects with three-body interactions

Quantum walks of interacting particles may display non-trivial features due to the interplay between the statistical nature and the many-body interactions associated to them. We analyze the quantum walk of interacting defects on top of an uniform bosonic Mott insulator at unit filling in an one dimensional graph. While the quantum walk of single particle defect shows trivial features, the case of two particles exhibits interesting phenomenon of quantum walk reversal as a function of additional onsite three-body attractive interactions. In the absence of the three-body interaction a quantum walk of pairs of particles is obtained and as the strength of the three-body interaction becomes more and more attractive, the independent particle behavior in quantum walk appears. Interestingly, further increase in the three-body interaction leads to the re-appearance of the quantum walk associated to a pair of particles. This quantum-walk reversal phenomenon is studied using the real-space density evolution, Bloch oscillation as well as two-particle correlation functions.

Reentrant s-wave superconductivity in the periodic Anderson model with attractive conduction band Hubbard interaction

Spin-flip scattering from magnetic impurities has a strong pair-breaking effect in s-wave superconductors where increasing the concentration of impurities rapidly destroys superconductivity. For small Kondo temperature TK the destruction of superconductivity is preceded by the reentrant superconductivity at finite temperature range Tc2 < T < Tc1, while the normal phase reappears at T < Tc2 ∼ TK. Here we explore the superconducting phase in a periodic system modeled as the Anderson lattice with additional attractive on-site (Hubbard) interaction g acting on the conduction band electrons. We solve the equations using dynamical mean field theory which incorporates Kondo physics, while the pairing interaction is treated on the static mean-field level. For large coupling g we find reentrant superconductivity which resembles the case with diluted impurities. However, we find evidence that reentrant superconductivity is here not a consequence of many-body correlations leading to the Kondo effect, but it rather stems from a competition between the single-particle hybridization and superconducting pairing. An insight into the spectral functions with in-gap structures is obtained from an approximate noninteracting dual model whose solution interpolates between several exact limits.

Collective-mode dispersion of atomic Fermi gases in a honeycomb optical lattice: Speed of sound of the attractive Kane–Mele–Hubbard model at half filling

We examine the superfluid states that emerge in the Kane–Mele model as a result of the on-site short-range attractive interaction U. The collective-mode dispersion is defined by the solutions of the Bethe–Salpeter (BS) equation in the generalized random phase approximation. The slope of the low-energy (Goldstone) mode and the corresponding sound velocity at half filling, calculated within the BS formalism, has been compared with the corresponding results obtained previously by the T-matrix approximation. The difference between the two approaches is that the T-matrix approximation takes into account only the ladder diagrams, and neglects the bubble ones. For this reason, the sound velocity in the direction toward point M, calculated within the T-matrix approximation, is about 4% less than the result obtained by employing the BS equation.

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.

Exact solution of the extended dimer Bose–Hubbard model with multi-body interactions

It is shown that the extended one-dimensional dimer Bose–Hubbard model with multi-body interactions can be solved exactly by using the algebraic Bethe ansatz mainly due to the site-permutation S2 symmetry. The solution for the model with up to three-particle hopping and three-body on-site interaction is explicitly shown. As an example of the application, lower part of the excitation energy levels and the ground-state entanglement measure of the standard Bose–Hubbard Hamiltonian with the attractive two-body on-site interaction plus the three-body on-site interaction for 100 bosons with variation of the control parameter are calculated by using the exact solution. It is shown that the attractive three-body on-site interaction reinforces the critical point entanglement of the system, which may be helpful for design of an optical lattice for ultracold atoms or a tuneable superconducting quantum interference device with maximal entanglement.

Numerically exact study of Weyl superconductivity

We study the interplay of interactions and topology in a pseudo-spin Weyl system, obtained from a minimally modified Hubbard model, using the numerically exact auxiliary-field quantum Monte Carlo method complemented by mean-field theory. We find that the pseudo-spin plays a key role in the pairing mechanism, and its effect is reflected in the structure of the pairing amplitude. An attractive on-site interaction leads to pairing between quasiparticles carrying opposite spin and opposite topological charge, resulting in the formation of real-spin singlet pairs that are a mixture of pseudo-spin singlet and pseudo-spin triplet. Our results provide a detailed characterization of the exotic pairing behavior in this system, and represent an important step towards a more complete understanding of superconductivity in the context of topological band structures, which will help guide searches for topological superconductivity in real materials and ultracold atoms.

Topological phase transition based on the attractive Hubbard model

We theoretically investigate the effect of an attractive on-site interaction on the two-band magnetic Dirac fermion model based on a square-lattice system. When the attractive fermion interaction is taken into account by the mean-field approximation, a phase diagram is obtained, furthermore it is found that a quantum phase transition from a band insulator state to the quantum anomalous Hall state occurs with increasing attractive interaction. For an existing quantum anomalous Hall state, the attractive interaction enlarges its nontrivial band gap and makes the topological edge states more localized, which protects the transport of linear-dispersive edge states against finite-size and further disorder effects.

Three-body constrained bosons in a double-well optical lattice

We analyse the ground-state properties of three-body constrained bosons in a one dimensional optical lattice with staggered hoppings analogous to the double well optical lattice. By considering attractive and repulsive on-site interactions between the bosons, we obtain the phase diagram which exhibits various quantum phases. Due to the double-well geometry and three-body constraint several gapped phases such as the Mott insulators and dimer/bond-order phases emerge at commensurate densities in the repulsive interaction regime. Attractive interaction leads to the pair formation which leads to the pair bond order phase at unit filling which resembles the valence-bond solid phase of composite bosonic pairs. At incommensurate densities we see the signatures of the gapless pair superfluid phase.

Dynamical vertex approximation for the attractive Hubbard model

In this work, we adapt the formalism of the dynamical vertex approximation (D$\Gamma$A), a diagrammatic approach including many-body correlations beyond the dynamical mean-field theory, to the case of attractive onsite interactions. We start by exploiting the ladder approximation of the D$\Gamma$A scheme, in order to derive the corresponding equations for the non-local self-energy and vertex functions of the attractive Hubbard model. Second, we prove the validity of our derivation by showing that the results obtained in the particle-hole symmetric case fully preserve the exact mapping between the attractive and the repulsive models. It will be shown, how this property can be related to the structure of the ladders, which makes our derivation applicable for any approximation scheme based on ladder diagrams. Finally, we apply our D$\Gamma$A algorithm to the attractive Hubbard model in three dimensions, for different fillings and interaction values. Specifically, we focus on the parameters region in the proximity of the second-order transition to the superconducting and charge-density wave phases, respectively, and calculate (i) their phase-diagrams, (ii) their critical behavior, as well as (iii) the effects of the strong non-local correlations on the single-particle properties.