Nearest-neighbor Repulsive 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.

Superconductivity from repulsive interactions on the kagome lattice

The discovery of superconductivity in layered vanadium-based kagome metals $A$V$_3$Sb$_5$ ($A$: K, Rb, Cs) has added a new family of materials to the growing class of possible unconventional superconductors. However, the nature of the superconducting pairing in these materials remains elusive. We present a microscopic theoretical study of the leading superconducting instabilities on the kagome lattice based on spin- and charge-fluctuation mediated Cooper pairing. The applied methodology includes effects of both on-site and nearest-neighbor repulsive Coulomb interactions. Near the upper van Hove filling -- relevant for the $A$V$_3$Sb$_5$ materials -- we find a rich phase diagram with several pairing symmetries being nearly degenerate. In particular, while a substantial fraction of the phase diagram is occupied by a spin-singlet order parameter transforming as a two-dimensional irreducible representation of the point group, several nodal spin-triplet pairing states remain competitive. We compute the band and interaction parameter-dependence of the hierarchy of the leading superconducting instabilities, and determine the detailed momentum dependence of the resulting preferred gap structures. Crucially, for moderate values of the interaction parameters, the individual pairing states depend strongly on momentum and exhibit multiple nodes on the Fermi surface. We discuss the properties of these superconducting gap structures in light of recent experimental developments of the $A$V$_3$Sb$_5$ materials.

Functional renormalization of spinless triangular-lattice fermions: N-patch vs. truncated-unity scheme

We study competing orders of spinless fermions in the triangular-lattice Hubbard model with nearest-neighbor interaction. We calculate the effective, momentum-resolved two-particle vertex in an unbiased way in terms of the functional renormalization group method and compare two different schemes for the momentum discretization, one based on dividing the Fermi surface into patches and one based on a channel decomposition. We study attractive and repulsive nearest-neighbor interaction and find a competition of pairing and charge instabilities. In the attractive case, a Pomeranchuk instability occurs at Van Hove filling and f-wave and p-wave pairing emerge when the filling is reduced. In the repulsive case, we obtain a charge density wave at Van Hove filling and extended p-wave pairing with reduced filling. The p-wave pairing solution is doubly degenerate and can realize chiral p+ip superconductivity with different Chern numbers in the ground state. We discuss implications for strongly correlated spin-orbit coupled hexagonal electron systems such as moiré heterostructures.Graphic

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.

Chiral bosonic topological insulator on the honeycomb lattice with anisotropic interactions

We study hard-core bosons on the honeycomb lattice in the presence of anisotropic nearest-neighbor repulsive interactions. Using a quantum Monte Carlo (QMC) technique, we extract the phase diagram of the model in terms of the filling and the anisotropy. At half-filling we find a dimer insulator phase near maximum anisotropy that is characterized by a finite topological entanglement entropy $\ln(2)/2$, indicative of a fractional quantum Hall state for bosons. We identify the presence of edge states and derive a QMC-based method to extract and verify their chirality. Remarkably, this phase arises in the absence of magnetic flux and without explicit lattice frustration.

Characterizing many-body localization via state sensitivity to boundary conditions

We introduce characterizations for many-body phase transitions between delocalized and localized phases based on the system's sensitivity to boundary conditions. In particular, we change boundary conditions from periodic to antiperiodic and calculate a shift in the system's energy and shifts in the single-particle density-matrix eigenvalues in the corresponding energy window. We employ the typical model for studying MBL, a one-dimensional disordered system of fermions with nearest-neighbor repulsive interaction where disorder is introduced as randomness on on-site energies. By calculating numerically the shifts in the system's energy and eigenvalues of the single-particle density matrix, we observe that in the localized regime, both shifts are vanishing; while in the extended regime, both shifts are on the order of the corresponding level spacing. We also applied these characterizations of the phase transition to the case of having next-nearest-neighbor interactions in addition to the nearest-neighbor interactions and studied its effect on the transition.

Conjecture on the Design of Helical Proteins.

In an important advance in our understanding of protein folding, Wolynes and Onuchic found that the frustration ratio, Tf/Ts, for funneled energy landscapes is Tf/Ts ∼1.6. In our recent work on four heme proteins, we showed that when a protein unfolds from the native state to an early unfolded state, the degree of departure is characterized by a ratio f ∼1.6, where f is a measure of the elongation of n-residue segments of the polypeptide chain. Our analysis, which accounts for this apparent similarity in calculated signatures, is based on a logistic-map model of unfolding. We offer an important take home for the de novo protein synthesis community: in order to increase the probability of obtaining good quality crystals, nearest-neighbor repulsive interactions between adjacent residues (or sequences of residues) in the polypeptide chain must be propagated correctly.

Dynamic magnetic hysteresis loop features of molecular-based magnetic materials and ferrimagnetic systems by the path probability method

Dynamic magnetic hysteresis loops (DMHL) features of molecular-based magnetic materials and ferrimagnetic systems are investigated by a mixed spin (1/2, 1) model by means of the path probability method (PPM). The PPM contains two rate constants; hence the DMHL features have been studied by using the method with two rate constants. In particular, the effects of the repulsive (J<0) and attractive (J>0) bilinear nearest-neighbor pair interactions, temperature (T), crystal-field interaction (D), angular frequency (ω) of the oscillating magnetic field and especially the rate constant (k2), which corresponds to the wheel speed in the melt spinning technique (MST), on the DMHL are investigated. The shapes and areas of hysteresis loops are affective sensibility by these system parameters. We also investigate the magnetic coercive fields and remanents magnetizations as a function ω. We found that the most of our results are in a good agreement with some theoretical and experimental reported works. We also observe the novel and interesting DMHL behaviors for lower values of T, and higher values of ω, k2 and D.

Haldane insulator in the 1D nearest-neighbor extended Bose-Hubbard model with cavity-mediated long-range interactions

In the one-dimensional Bose-Hubbard model with on-site and nearest-neighbor interactions, a gapped phase characterized by an exotic non-local order parameter emerges, the Haldane insulator. Bose-Hubbard models with cavity-mediated global range interactions display phase diagrams, which are very similar to those with nearest-neighbor repulsive interactions, but the Haldane phase remains elusive there. Here we study the one-dimensional Bose-Hubbard model with nearest-neighbor and cavity-mediated global-range interactions and scrutinize the existence of a Haldane Insulator phase. With the help of extensive quantum Monte-Carlo simulations we find that in the Bose-Hubbard model with only cavity-mediated global-range interactions no Haldane phase exists. For a combination of both interactions, the Haldane Insulator phase shrinks rapidly with increasing strength of the cavity-mediated global-range interactions. Thus, in spite of the otherwise very similar behavior the mean-field like cavity-mediated interactions strongly suppress the non-local order favored by nearest-neighbor repulsion in some regions of the phase diagram.Graphical abstract

Quantifying the fragility of unprotected quadratic band crossing points

We examine a basic lattice model of interacting fermions that exhibits quadratic band crossing points (QBCPs) in the non-interacting limit. In particular, we consider spinless fermions on the honeycomb lattice with nearest neighbor hopping $t$ and third-nearest neighbor hopping $t''$, which exhibits fine-tuned QBCPs at the corners of the Brillouin zone for ${t'' = t/2}$. In this situation, the density of states remains finite at the Fermi level of the half-filled band and repulsive nearest-neighbor interactions $V$ lead to a charge-density-wave (CDW) instability at infinitesimally small $V$ in the random-phase approximation or mean-field theory. We examine the fragility of the QBCPs against dispersion renormalizations in the ${t\mbox{-}t''\mbox{-}V}$ model using perturbation theory, and find that the $t''$-value needed for the QBCPs increases with $V$ due to the hopping renormalization. However, the instability toward CDW formation always requires a nonzero threshold interaction strength, i.e., one cannot fine-tune $t''$ to recover the QBCPs in the interacting system. These perturbative arguments are supported by quantum Monte Carlo simulations for which we carefully compare the corresponding threshold scales at and beyond the QBCP fine-tuning point. From this analysis, we thus gain a quantitative microscopic understanding of the fragility of the QBCPs in this basic interacting fermion system.

Exclusion process on an open lattice with fluctuating boundaries

We show that the TASEP of a driven system of particles of arbitrary size, with nearest neighbor repulsive interaction, on an open lattice is equivalent to the TASEP of interacting monomers on an open lattice whose size fluctuates in response to the entry and exit of particles. We have presented the maximal current profile as a function of the interaction strength for dimers and tetramers, obtained in Monte Carlo simulation; the results agree well with the ones computed by applying a specific rod-to-monomer mapping to the steady state current and density predicted by a mean-field theory of interacting monomers which adapts a Markov Chain approach for incorporating nearest-neighbor correlations.

Entanglement entropy distribution in the strongly disordered one-dimensional Anderson mode

The entanglement entropy (EE) distribution of strongly disordered one dimensional spin chains, which are equivalent to spinless fermions at half-filling on a bond (hopping) disordered one-dimensional Anderson model, has been shown to exhibit very distinct features such as peaks at integer multiplications of , essentially counting the number of singlets traversing the boundary. Here we show that for a canonical Anderson model with box distribution on-site disorder and repulsive nearest-neighbor interactions the EE distribution also exhibits interesting features, albeit different than the distribution seen for the bond disordered Anderson model. The canonical Anderson model shows a broad peak at low entanglement values and one narrower peak at . Density matrix renormalization group calculations reveal this structure and the influence of the disorder strength and the interaction strength on its shape. A modified real space renormalization group method was used to get a better understanding of this behavior. As might be expected the peak centered at low values of EE has a tendency to shift to lower values as disorder is enhanced. A second peak appears around the EE value of , this peak is broadened and no additional peaks at higher integer multiplications of are seen. We attribute the differences in the distribution between the canonical model and the broad hopping disorder to the influence of the on-site disorder which breaks the symmetry across the boundary.

Competing superconducting phases in the interacting two-dimensional electron gas with strong Rashba spin-orbit coupling

In this work we study interacting electrons on square lattice in the presence of strong Rashba spin-orbit interaction. The spin-orbit term forces the time-reversal electron states to be paired in even Cooper channels. For concreteness, we only consider the repulsive onsite Hubbard and nearest-neighbor coulomb interactions, the so called extended Hubbard model. To examine the superconducting instability we obtain the effective interaction between electrons within the random phase approximation and treat the pairing instabilities driven by charge and spin fluctuations and their combined effects. We mapped out the phase diagram of the model in terms of interactions and electron fillings, and found that while the $d_{xy}$ and $d_{x^2-y^2}$ symmetries are the most likely pairing symmetries driven by charge and spin fluctuations, respectively, the strong effect of both fluctuations yields higher angular momentum Cooper instability. The possibility of topological superconductivity and triplet pairing is also discussed.

Spontaneous symmetry breaking of an interacting Chern insulator on a topological square lattice

The interplay between topology and correlation lies at the forefront of modern condensed matter physics. In this paper, we study the extended fermion-Hubbard model, including the on-site as well as the nearest-neighbor repulsive interactions, on a topological square lattice that supports the Chern insulator. Within the mean-field method, we find that the spontaneous symmetry breaking (SSB) charge-density wave or antiferromagnetic insulator dominates the system when the onsite or nearest-neighbor interactions are strong enough. It is interesting that the antiferromagnetic Chern insulator will appear in the phase diagram when there is an explicitly nonvanishing sublattice potential. In addition, we explore how a finite-size ribbon structure affects the phase diagram and point out that the critical interaction for SSB occurs with weaker strength than the bulk system.

Quantum anomalous Hall phase stabilized via realistic interactions on a kagome lattice

We study the quantum phases of spinless fermion at one-third filling on a Kagome lattice featuring a quadratic band touching Fermi point. In the presence of weak first and second nearest-neighbor repulsive interactions ($V_1$ and $V_2$), we demonstrate an interaction driven quantum anomalous Hall effect by employing exact diagonalization and density-matrix renormalization group methods. The time-reversal symmetry is broken spontaneously by forming loop currents that exhibit long-range correlation. Quantized Hall conductance corresponding to Chern number of $\pm1$ is obtained by measuring the pumped charge through inserting flux in a cylinder geometry. We find that the energy gap, which topologically protects the emerging ground states, can be enhanced remarkably by a moderate $V_2 < V_1$ via calculating the spectrum and charge excitation gaps, which highlights the experimentally feasible scheme of realizing interaction driven topological phase by spatially decaying interactions on topologically trivial lattice models.

Diffusion on a one-dimensional sawtooth lattice with the nearest and the next nearest neighbor interactions

The diffusion of particles adsorbed on a homogeneous one-dimensional sawtooth lattice with the nearest neighbor and the next nearest neighbor interactions between the particles is investigated using a theoretical approach and the kinetic Monte Carlo simulations. I have derived the analytical expressions for the diffusion coefficients. The calculated concentration dependencies of the coefficients have been compared with the numerical data generated by the simulations. The comparison reveals an interesting peculiarity of the particle diffusion. The lateral interactions induce correlations in the successive jumps of the particles. The thorough investigations of the dependencies clearly demonstrate how with the strengthening of the interactions the classical uncorrelated jumps are gradually replaced by the sequences of the correlated jumps. This behavior principally differs from the usual diffusion of particles in the homogeneous one-dimensional systems. It is an interesting and unexpected novelty of this system. Another uncommon feature of this model is a rich variety of the ‘diffusion coefficients’. There are four combinations of the interaction parameter signs, and every combination has its own specific behavior of the particle diffusion, qualitatively opposite from the other combinations. Also, it should be noted a quite unusual result. In the homogeneous lattice gas system (all sites have an equal depth) with the strong, repulsive nearest neighbor and attractive next nearest neighbor interactions the diffusion is perfectly described by the diffusion coefficients derived for the heterogeneous lattices with deep and shallow sites. It is a direct evidence of the specific mode of the particle migration when the correlated pairs of jumps give the main contribution to the diffusion coefficients.

Bond-ordered states and f -wave pairing of spinless fermions on the honeycomb lattice

Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behaviour in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the van-Hove filling, the free Fermi surface is hole-like and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the van-Hove filling the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling the free Fermi surface becomes electron-like and a superconducting instability with $f$-wave symmetry is found to emerge from the interplay of intra-unitcell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.

Impurity and soliton dynamics in a Fermi gas with nearest-neighbor interactions

We study spinless fermions with repulsive nearest-neighbor interactions perturbed by an impurity particle or a local potential quench. Using the numerical time-evolving block decimation method and a simplified analytic model, we show that the pertubations create a soliton-antisoliton pair. If solitons are already present in the bath, the two excitations have a drastically different dynamics: The antisoliton does not annihilate with the solitons and is therefore confined close to its origin while the soliton excitation propagates. We discuss the consequences for experiments with ultracold gases.

A supersolid phase of hardcore boson in square optical superlattice

We have applied Quantum Monte Carlo technique to study the supersolid phase of hardcore bosons with nearest-neighbor repulsive interactions (NNRI) on square superlattice forming by an external potential. In a same NNRI model investigated by Batrouni et al. [Phys. Rev. Lett. 84, 1599 (2000)], there is no supersolid phase but phase separation. In this study, we have found the supersolid phase in the wide range of particle density with an assistance of the sufficient large external potential. Interestingly, a supersolid phase exists, on both the vacancy and interstitial sides. We have not found supersolid phase simultaneously existing with the crystals at any particle density. In the limit of a weak external potential strength, the system keeps all the features of the square lattice model which is similar to the model without an external potential. Increasing the external potential strength will induce the crystal phases at different filling factors commensurate with the external potential, i.e. ρ = 1 / 3 and 2/3 away from half filling. A strong external potential can even blow out the checkerboard crystal at half filling. The other possible relevance of these results to experiments on other similar systems such as the ultracold atom traping in optical lattice are discussed.

Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional renormalization group calculation with high-wave-vector resolution

We investigate the quantum many-body instabilities for electrons on the honeycomb lattice at half-filling with extended interactions, motivated by a description of graphene and related materials. We employ a recently developed fermionic functional Renormalization Group scheme which allows for highly resolved calculations of wavevector dependences in the low-energy effective interactions. We encounter the expected anti-ferromagnetic spin density wave for a dominant on-site repulsion between electrons, and charge order with different modulations for dominant pure $n$-th nearest neighbor repulsive interactions. Novel instabilities towards incommensurate charge density waves take place when non-local density interactions among several bond distances are included simultaneously. Moreover, for more realistic Coulomb potentials in graphene including enough non-local terms there is a suppression of charge order due to competition effects between the different charge ordering tendencies, and if the on-site term fails to dominate, the semi-metallic state is rendered stable. The possibility of a topological Mott insulator being the favored tendency for dominating second nearest neighbor interactions is not realized in our results with high momentum resolution.