Attractive Nearest-neighbor Interactions Research Articles

CDMFT+HFD: An extension of dynamical mean field theory for nonlocal interactions applied to the single band extended Hubbard model

We examine the phase diagram of the extended Hubbard model on a square lattice, for both attractive and repulsive nearest-neighbor interactions, using CDMFT+HFD, a combination of Cluster Dynamical Mean Field theory (CDMFT) and a Hartree-Fock mean-field decoupling of the inter-cluster extended interaction. For attractive non-local interactions, this model exhibits a region of phase separation near half-filling, in the vicinity of which we find islands of d-wave superconductivity, decaying rapidly as a function of doping, with disconnected regions of extended s-wave order at smaller (higher) electron densities. On the other hand, when the extended interaction is repulsive, a Mott insulating state at half-filling is destabilized by hole doping, in the strong-coupling limit, in favor of d-wave superconductivity. At the particle-hole invariant chemical potential, we find a first-order phase transition from antiferromagnetism (AF) to d-wave superconductivity as a function of the attractive nearest-neighbor interaction, along with a deviation of the density from the half-filled limit. A repulsive extended interaction instead favors charge-density wave (CDW) order at half-filling.

Emergent Mott insulators at noninteger fillings and devil's staircase induced by attractive interaction in many-body polarons

We investigate the ground-state properties of an ultracold-atom system consisting of many-body polarons, quasiparticles formed by impurity atoms in optical lattices immersed in a Bose-Einstein condensate. We find the nearest-neighbor attractive interaction between polarons can give rise to rich physics that is peculiar to this system. In a relatively shallow optical lattice, the attractive interaction can drive the system to be in a self-bound superfluid phase, with its particle density distribution manifesting a self-concentrated structure. However, in a relatively deep optical lattice, the attractive interaction can drive the system, leading to the Mott-insulator phase even though the global filling factor is not an integer. Interestingly, in the Mott-insulator regime, the system can support a series of different Mott insulators, with their effective density manifesting a devil's-staircase structure with respect to the strength of the attractive interaction. A detailed estimation of the relevant experimental parameters shows that these rich physics can be readily observed in current experimental setups.

Revisiting superconductivity in the extended one-band Hubbard model: Pairing via spin and charge fluctuations

The leading superconducting instabilities of the two-dimensional extended repulsive one-band Hubbard model within spin-fluctuation pairing theory depend sensitively on electron density, band, and interaction parameters. We map out the phase diagrams within a random-phase-approximation spin- and charge-fluctuation approach, and find that while ${B}_{1g}$ (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) and ${B}_{2g}$ (${d}_{xy}$) pairing dominates in the absence of repulsive longer-range Coulomb interactions ${V}_{\mathrm{NN}}$, the latter induces pairing in other symmetry channels, including, e.g., ${A}_{2g}$ ($g$-wave), nodal ${A}_{1g}$ (extended $s$-wave), or nodal ${E}_{u}$ ($p$-wave) spin-triplet superconductivity. At the lowest temperatures, transition boundaries in the phase diagrams between symmetry-distinct spin-singlet orders generate complex time-reversal symmetry broken superpositions. By contrast, we find that boundaries between singlet and triplet regions are characterized by first-order transitions. Finally, motivated by recent photoemission experiments, we have determined the influence of an additional explicitly attractive nearest-neighbor interaction, ${V}_{\mathrm{NN}}<0$, on the superconducting gap structure. Depending on the electronic filling, such an attraction boosts ${E}_{u}$ ($p$-wave) spin-triplet or ${B}_{1g}$ (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) spin-singlet ordering.

Perpendicular and parallel phase separation in two-species driven diffusive lattice gases.

We study three different lattice models in which two species of diffusing particles are driven in opposite directions by an electric field. We focus on dynamical phase transitions that involve phase separation into domains that may be parallel or perpendicular to a driving field. In all cases, the perpendicular state appears for weak driving, consistent with previous work. For strong driving, we introduce two models that support the parallel state. In one model, this state occurs because of the inclusion of dynamical rules that enhance lateral diffusion during collisions; in the other, it is a result of a nearest-neighbor attractive or repulsive interaction between particles of the same or opposite species. We discuss the connections between these results and the behavior found in off-lattice systems, including laning and freezing by heating.

Phase diagram of superconductivity in the integer quantum Hall regime

An interplay between pairing and topological orders has been predicted to give rise to superconducting states supporting exotic emergent particles, such as Majorana particles obeying non-Abelian braid statistics. We consider a system of spin polarized electrons on a Hofstadter lattice with nearest-neighbor attractive interaction and solve the mean-field Bogoliubov-de Gennes equations in a self-consistent fashion, leading to gauge-invariant observables and a rich phase diagram as a function of the chemical potential, the magnetic field, and the interaction. As the strength of the attractive interaction is increased, the system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully gapped in the bulk but has topological chiral edge current, characterizing a topologically nontrivial state. This is followed by a vortex phase in which the vortices carrying Majorana modes form a lattice; the spectrum contains a low-energy Majorana band arising from the coupling between neighboring vortex-core Majorana modes but does not have chiral edge currents. For some parameters, a dimer vortex lattice occurs with no Majorana band. The experimental feasibility and the observable consequences of skyrmions as well as Majorana modes are indicated.

Fermi arcs and pseudogap phase in a minimal microscopic model of d -wave superconductivity

We show conclusively that a pseudogap state can arise at $T > T_c$, for reasonable pairing interaction strength, from order parameter fluctuations in a two dimensional minimal model of $d$-wave superconductivity. The occurrence of the pseudogap requires neither strong correlation nor the presence of competing order. We study a model with attractive nearest neighbor interaction and establish our result using a combination of cluster based Monte Carlo for the order parameter field and a twisted-boundary scheme to compute the momentum-resolved spectral function. Apart from a dip in the density of states that characterizes the pseudogap, the momentum and frequency resolution on our effective lattice size $\sim 160 \times 160$ allows two major conclusions: (i)~at $T < T_c$, despite the presence of thermal phase fluctuations the superconductor has only nodal Fermi points while all non nodal points on the normal state Fermi surface show a two peak spectral function with a dip at $\omega =0$, and (ii)~for $T > T_c$ the Fermi points develops into arcs, characterized by a single quasiparticle peak, and the arcs connect up to recover the normal state Fermi surface at a temperature $T^* > T_c$. We show the variation of $T_c$ and $T^*$ with coupling strength and provide detailed spectral results at a coupling where $T^* \sim 1.5T_c$.

Trapping in self-avoiding walks with nearest-neighbor attraction.

The statistics of self-avoiding random walks have been used to model polymer physics for decades. A self-avoiding walk that grows one step at a time on a lattice will eventually trap itself, which occurs after an average of 71 steps on a square lattice. Here, we consider the effect of nearest-neighbor attractive interactions on isolated growing self-avoiding walks, and we examine the effect that self-attraction has both on the statistics of trapping as well as on chain statistics through the transition between expanded and collapsed walks at the theta point. We find that the trapping length increases exponentially with the nearest-neighbor contact energy, but that there is a local minimum in trapping length for weakly self-attractive walks. While it has been controversial whether growing self-avoiding walks have the same asymptotic behavior as traditional self-avoiding walks, we find that the theta point is not at the same location for growing self-avoiding walks, and that the persistence length converges much more rapidly to a smaller value.

Emergent bosons in the fermionic two-leg flux ladder

We study the emergence of bosonic pairs in a system of two coupled one-dimensional fermionic chains subject to a gauge flux (two-leg flux ladder), with both attractive and repulsive interaction. In the presence of strong attractive nearest-neighbor interaction and repulsive next-to-nearest-neighbor interaction, the system crosses into a regime in which fermions form tightly bound pairs, which behave as bosonic entities. By means of numerical simulations based on the density-matrix-renormalization-group (DMRG) method, we show in particular that in the strongly paired regime, the gauge flux induces a quantum phase transition of the Ising type from vortex density wave (VDW) to a charge density wave (CDW), characteristic of bosonic systems.

Transverse temperature interfaces in the Katz-Lebowitz-Spohn driven lattice gas.

We explore the intriguing spatial patterns that emerge in a two-dimensional spatially inhomogeneous Katz-Lebowitz-Spohn (KLS) driven lattice gas with attractive nearest-neighbor interactions. The domain is split into two regions with hopping rates governed by different temperatures T>T_{c} and T_{c}, respectively, where T_{c} indicates the critical temperature for phase ordering, and with the temperature boundaries oriented perpendicular to the drive. In the hotter region, the system behaves like the (totally) asymmetric exclusion processes (TASEP), and experiences particle blockage in front of the interface to the critical region. To explain this particle density accumulation near the interface, we have measured the steady-state current in the KLS model at T>T_{c} and found it to decay as 1/T. In analogy with TASEP systems containing "slow" bonds, we argue that transport in the high-temperature subsystem is impeded by the lower current in the cooler region, which tends to set the global stationary particle current value. This blockage is induced by the extended particle clusters, growing logarithmically with system size, in the critical region. We observe the density profiles in both high- and low-temperature subsystems to be similar to the well-characterized coexistence and maximal-current phases in (T)ASEP models with open boundary conditions, which are respectively governed by hyperbolic and trigonometric tangent functions. Yet if the lower temperature is set to T_{c}, we detect marked fluctuation corrections to the mean-field density profiles, e.g., the corresponding critical KLS power-law density decay near the interfaces into the cooler region.

Influence of the symmetry of hybridization on the critical temperature of multiband superconductors

In this paper, we study a two-band model of a superconductor in a square lattice. One band is narrow in energy and includes local Coulomb correlations between its quasiparticles. Pairing occurs in this band due to nearest-neighbor attractive interactions. Extended $s$-wave as well as $d$-wave symmetries of the superconducting order parameter are considered. The correlated electrons hybridize with those in another wide conduction band through a $k$-dependent mixing with even or odd parity depending on the nature of the orbitals. The many-body problem is treated within a slave-boson approach that has proved adequate to deal with the strong electronic correlations that are assumed here. Since applied pressure changes mostly the ratio between hybridization and bandwidths, we can use this ratio as a control parameter to obtain the phase diagrams of the model. We find that, for a wide range of parameters, the critical temperature increases as a function of hybridization (pressure) with a region of first-order transitions. When frustration is introduced, it gives rise to a stable superconducting phase. We find that superconductivity can be suppressed for specific values of band filling due to the Coulomb repulsion. We show how pressure, composition, and strength of correlations affect the superconductivity for different symmetries of the order parameter and the hybridization.

Kirkendall effect in the two-dimensional lattice-gas model

Customarily, the Kirkendall effect is associated with the vacancy-mediated balance of diffusion fluxes of atoms at the interface between two metals. Nowadays, this effect attracts appreciable attention due to its crucial role in the formation of various hollow nanoparticles via oxidation of metal nanocrystallites. The understanding of the physics behind this effect in general and especially in the case of nanoparticles is still incomplete due to abundant complicating factors. Herein, the Kirkendall effect is illustrated in detail at the generic level by performing two-dimensional (2D) lattice Monte Carlo simulations of diffusion of A and B monomers with attractive nearest-neighbor interaction for times up to 10^{7} Monte Carlo steps. Initially, A monomers are considered to form a close-packed array, while B monomers are in the 2D-gas state. The A-B interaction is assumed to be stronger compared to the other interactions, so that thermodynamically the c(2×2) A-B phase is preferable compared to the close-packed A phase (as in the case of metal oxidation). Depending on the relative rate of the diffusion jumps of A and B monomers, the patterns observed at the late stage of the formation of the mixed phase are shown to range from a single array without voids to those with appreciable disintegration of the initial array. In this way, the model predicts a single array with numerous small voids, a few moderate voids, or a single large void inside.

Phase diagrams of singlet superconducting states with mixed symmetry

The competition between the singlet superconducting states with s- and d-wave symmetry of the order parameter is studied within a single-band model with nearest-neighbor attractive interaction. The ground state and finite-temperature phase diagrams are constructed for different ratios between the nearest- and next-nearest-neighbor electron transfer integrals. The mixed s+id pairing state is shown to be formed in the intermediate region between s- and d-waves. The temperature phase transitions between the pure and the mixed pairing state are found.

Quantum phases of constrained dipolar bosons in coupled one-dimensional optical lattices

We investigate a system of two- and three-body constrained dipolar bosons in a pair of one-dimensional optical lattices coupled to each other by the non-local dipole-dipole interactions. Assuming attractive dipole-dipole interactions, we obtain the ground state phase diagram of the system by employing the cluster mean-field theory. The competition between the repulsive on-site and attractive nearest-neighbor interactions between the chains yields three kinds of superfluids; namely the trimer superfluid, pair superfluid and the usual single particle superfluid along with the insulating Mott phase at the commensurate density. Besides, we also realize simultaneous existence of Mott insulator and superfluid phases for the two- and three-body constrained bosons, respectively. We also analyze the stability of these quantum phases in the presence of a harmonic trap potential.

Capacitance and compressibility of heterostructures with strong electronic correlations

Strong electronic correlations related to a repulsive local interaction suppress the electronic compressibility in a single-band model, and the capacitance of a corresponding metallic film is directly related to its electronic compressibility. Both statements may be altered significantly when two extensions to the system are implemented which we investigate here: (i) we introduce an attractive nearest-neighbor interaction $V$ as antagonist to the repulsive on-site repulsion $U$, and (ii) we consider nano-structured multilayers (heterostructures) assembled from two-dimensional layers of these systems. We determine the respective total compressibility $\kappa$ and capacitance $C$ of the heterostructures within a strong coupling evaluation, which builds on a Kotliar-Ruckenstein slave-boson technique. Whereas the capacitance $C(n)$ for electronic densities $n$ close to half-filling is suppressed---illustrated by a correlation induced dip in $C(n)$---it may be appreciably enhanced close to a van Hove singularity. Moreover, we show that the capacitance may be a non-monotonic function of $U$ close to half-filling for both attractive and repulsive $V$. The compressibility $\kappa$ can differ from $C$ substantially, as $\kappa$ is very sensitive to internal electrostatic energies which in turn depend on the specific set-up of the heterostructure. In particular, we show that a capacitor with a polar dielectric has a smaller electronic compressibility and is more stable against phase separation than a standard non-polar capacitor with the same capacitance.

Study on the ground states of a square-lattice polymer by using exhaustive enumeration

We exhaustively enumerate the ground-state conformations of polymers with attractive nearest-neighbor interactions on a square lattice. We find that when the ground-state number is considered as a function of the chain length, local minima appear at magic lengths. However, the ground-state entropy per monomer does not vanish in the thermodynamic limit when an extrapolation is performed with the magic-length data, implying that the number of ground-state conformations grows exponentially. We also study the entropy difference between the ground and the first-excited states. The entropy difference per monomer diverges in the thermodynamic limit, indicating that the zero-tail of the specific heat is modified in the thermodynamic limit.

Cooperon condensation and intravalley pairing states in honeycomb Dirac systems

Motivated by recent developments in the experimental study of superconducting graphene and transition metal dichalcogenides, we investigate superconductivity of the Kane-Mele (KM) model with short-range attractive interactions on the two-dimensional honeycomb lattice. We show that intra-valley spin-triplet pairing arises from nearest-neighbor (NN) attractive interaction and the intrinsic spin-orbit coupling. We demonstrate this in two independent approaches: We study superconducting instability driven by condensation of Cooperons, which are in-gap bound states of two conduction electrons, within the $T$-matrix approximation and also study the superconducting ground state within the mean-field theory. We find that Cooperons with antiparallel spins condense at the $K$ and $K'$ points. This leads to the emergence of an intra-valley spin-triplet pairing state belonging to the irreducible representation A$_1$ of the point group $C_{6v}$. The fact that this pairing state has opposite chirality for $K$ and $K'$ identifies this state as a "helical" valley-triplet state, the valley-analog to the $^3$He-B phase in two dimension. Because of the finite center of mass momentum of Cooper pairs, the pair amplitude in NN bonds exhibits spatial modulation on the length scale of lattice constant, such that this pairing state may be viewed as a pair-density wave state. We find that the pair amplitude spontaneously breaks the translational symmetry and exhibits a $p$-Kekul\'e pattern. We also discuss the selection rule for pairing states focusing the characteristic band structure of the KM model and the Berry phase effects to the emergence of the intra-valley pairing state.

Two-dimensional Ostwald ripening on a patterned support and in a mixed overlayer

The author presents lattice Monte Carlo simulations of Ostwald ripening of islands formed of monomers with attractive nearest-neighbor interaction in two situations. The first one implies that monomers of one kind are located on a heterogeneous support which itself includes embedded frozen patterns of the Ostwald type. This feature is demonstrated to be able to terminate the island ripening. In the second case, the support is considered to be uniform while the overlayer is assumed to contain monomers of two kinds. This complicating factor is found to nearly not modify the ripening kinetics or make it somewhat slower despite appreciable correlations in the arrangement of different monomers.

Topological states with broken translational and time-reversal symmetries in a honeycomb-triangular lattice

We study fermions in a lattice, with on-site and nearest neighbor attractive interactions between two spin species. We consider two geometries: both spins in a triangular lattice, and a mixed geometry with up-spins in honeycomb and down-spins in triangular lattices. We focus on the interplay between spin-population imbalance, on-site and valence bond pairing, and order parameter symmetry. The mixed geometry leads to a rich phase diagram of topologically non-trivial phases. In both geometries, we predict order parameters with simultaneous time-reversal and translational symmetry breaking.

Low-temperature conformational transition of a square-lattice polymer

We study the low-temperature transition of polymers with attractive nearest-neighbor interactions on a square lattice. Measuring the specific heat obtained by using the exact number of possible conformations for each energy value, we find a peak in the low-temperature region, distinct from the peak corresponding to the coil-globule transition. We find that the low-temperature peak becomes prominent for specific polymer lengths called the magic lengths, for which the ground state forms a square or a rectangle. The low-temperature peaks for magic lengths are more intense than those for other lengths and appear at lower temperatures.

Cross-circularly polarized two-exciton states in one to three dimensions.

Biexciton and two-exciton dissociated states of Frenkel-type excitons are studied theoretically using an exciton tight-binding (TB) model including a polarization degree of freedom. Because the biexciton consists of two cross-circularly polarized excitons, an on-site interaction (V) between the two excitons should be considered in addition to a nearest-neighbor two-exciton attractive interaction (δ). Although there are an infinitely large number of combinations of V and δ providing the observed binding energy of a biexciton, the wave function of the biexciton and two-exciton dissociated states is nearly independent of these parameter sets. This means that all the two-exciton states are uniquely determined from the exciton TB model. There are a spatially symmetric and an antisymmetric biexciton state for a one-dimensional (1D) lattice and two symmetric and one antisymmetric biexciton states at most for two- (2D) and three-dimensional (3D) lattices. In contrast, when the polarization degree of freedom is ignored, there is one biexciton state for 1D, 2D, and 3D lattices. For this study, a rapid and memory-saving calculation method for two-exciton states is extended to include the polarization degree of freedom.