Electron instabilities in the Hubbard model with the next nearest neighbor coupling are calculated by exact diagonalization in finite, two-dimensional Betts cells (lattices). A viable spin and charge coherent pairing, signaled by quantum critical points and a negative charge gap region, is found in 8- and 10-site Betts lattices at small and moderate U regions consistent with our exact results in elementary bipartite geometries [Phys. Rev. B 78 (2008) 075431]. The contour isolines for continuous temperature driven-crossover between the Mott-Hubbard insulating and coherent pairing phases are demonstrated. The criteria for smooth and abrupt phase transitions are found for systematic enhancement of coherent pairing by optimization of the next nearest neighbor coupling parameter.
We study the possible superconducting pairing symmetry mediated by spin and charge fluctuations on the honeycomb lattice using the extended Hubbard model and the random-phase-approximation method. From $2\%$ to $20\%$ doping levels, a spin-singlet $d_{x^{2}-y^{2}}+id_{xy}$-wave is shown to be the leading superconducting pairing symmetry when only the on-site Coulomb interaction $U$ is considered, with the gap function being a mixture of the nearest-neighbor and next-nearest-neighbor pairings. When the offset of the energy level between the two sublattices exceeds a critical value, the most fav…
The nearest-neighbor superexchange-mediated mechanism for d_{x^2-y^2}-wave superconductivity in the one-band Hubbard model faces the challenge that nearest-neighbor Coulomb repulsion can be larger than superexchange. To answer this question, we use cellular dynamical mean-field theory (CDMFT) with a continuous-time quantum Monte Carlo solver to determine the superconducting phase diagram as a function of temperature and doping for on-site repulsion $U=9t$ and nearest-neighbor repulsion $V=0,2t,4t$. In the underdoped regime, $V$ increases the CDMFT superconducting transition temperature $T_c^d$…
Recently, the experimental results by the angle-resolved photoemission spectroscopy suggested that an additional strong nearest neighbor attraction in the Hubbard model might be significant to describe the properties of doped cuprates more accurately. The stripe-ordered patterns, formed by the inhomogeneous distribution of spin, charge and pairing correlations in the CuO$_{2}$ planes, is a known feature of doped cuprates. In this work, the effect of the nearest neighbor attraction and the stripe phase are examined by using the constrained path quantum Monte Carlo method within the repulsive Hu…
We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest neighbour range. In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbour and next-nearest-neighbour interactions. Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations. The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably ri…
Motivated by the surge in research activities on graphene, we investigate instabilities of electrons on the honeycomb lattice, interacting by onsite and nearest-neighbor terms, using a renormalization group scheme. Near half band-filling, critical minimal interaction strengths are required for instabilities toward antiferromagnetic or charge-density wave order. Away from half filling, f-wave triplet pairing and d+id singlet pairing instabilities are found to emerge out of density-wave regimes.
Motivated by the recent discovery of the anomalously nearest-neighbor attraction arising from the electron-phonon coupling, we quantitatively investigate the enhancing effects of this additional attractive channel on the $d$-wave SC based on dynamic cluster quantum Monte Carlo calculations of doped two-dimensional extended Hubbard model with nearest-neighbor attraction $-V$. Focusing on the range of $0<-V/t \le 2$, our simulations indicate that the dynamics of $d$-wave projected pairing interaction is attractive at all frequencies and increases with $|V|$. Moreover, turning on $-V$ attraction …
We investigate the effects of the next-nearest-neighbor ($t'$) and the third-nearest-neighbor (t") hopping terms on superconductivity (SC) correlation in the 2D hole-doped extended t-J model based on the variational Monte-Carlo (VMC), mean-field (MF) calculation, and exact diagonalization (ED) method. Despite of the diversity of the methods employed, the results all point to a consistent conclusion: While the d-wave SC correlation is slightly suppressed by t' and t" in underdoped regions, it is greatly enhanced in the optimal and overdoped regions. The optimal T_c is a result upon balance of t…
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 oc…
Motivated by the presence of various charge inhomogeneities in strongly correlated systems of coupled ladders, a model of spatially separated bosonic and fermionic degrees of freedom is numerically studied. In this model, bosonic chains are connected to fermionic chains by two types of generalized Andreev couplings. It is shown that for both types of couplings the long-distance pairing correlations are enhanced. Near quarter filling, this effect is much larger for the splitting of a pair in electrons which go to the two neighboring fermionic chains than for a pair hopping process. It is argued…
We investigate superconducting pairing driven by electron-electron interactions in a theoretical model for monolayer MoS$_2$ with the temperature-flow functional renormalization group(fRG). At low doping, the dominant instability is toward odd-parity pairing with $f$-wave Mo-nearest-neighbor structure. We compute the fRG phase diagram versus electron doping below the van Hove filling of the conduction band. In the superconducting regime, the critical temperature grows with doping, comparable to the experiments. Near van Hove filling the system favors a ferromagnetic state. We demonstrate that …
We investigate the spin fluctuations and the pairing symmetry in A$_{x}$Fe$_{2-y}$Se$_{2}$ by the fluctuation exchange approximation. Besides the on-site interactions, the next-nearest-neighbor antiferromagnetic coupling $J_{2}$ is also included. We find that both the itinerant and the localized natures of electrons are important to describe the recent experimental results of the spin fluctuations and the pairing symmetry. In particular, a small $J_{2}$ coupling can change the pairing gap from the d-wave symmetry to the s-wave symmetry. We have also studied the real-space structures of the gap…
We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (U) and nearest-neighbor (V) interactions, at weak couplings. We show that the charge-density-wave phase that is known to occur at half-filling when 4V > U gives way to a d_{xy} -wave superconducting instability away from half-filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive and a range of on-site repulsive interaction. In addition, when nesting is further suppressed and in presence of a nearest-neighbor attraction, a triplet time-reversal…
We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t=-0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle …
We develop a DCA(PQMC) algorithm which employs the projective quantum Monte Carlo (PQMC) method for solving the equations of the dynamical cluster approximation (DCA) at zero temperature, and apply it for studying pair susceptibilities of the two-dimensional Hubbard-model with next-nearest neighbor hopping. In particular, we identify which pairing symmetry is dominant in the U-n parameter space (U: repulsive Coulomb interaction; n: electron density). We find that p_{x+y}- (d_{x^2-y^2}-) wave is dominant among triplet (singlet) pairings -at least for 0.3<n<0.8 and U<=4t. The crossover between d…
We study spin-half fermions in a one-dimensional extended Hubbard chain at low filling. We identify three triplet and one singlet pairing channels in the system, which are independently tunable as a function of nearest-neighbor charge and spin interactions. In a large-size system with translational invariance, we derive gap equations for the corresponding pairing gaps and obtain a Bogoliubov-de Gennes Hamiltonian with its non-trivial topology determined by the interplay of these gaps. In an open-end system with a fixed number of particles, we compute the exact many-body ground state and identi…
We show that finite angular momentum pairing chiral superconductors on the triangular lattice have point zeroes in the complex gap function. A topological quantum phase transition takes place through a nodal superconducting state at a specific carrier density $x_c$ where the normal state Fermi surface crosses the isolated zeros. For spin singlet pairing, we show that the second nearest neighbor $d+id$-wave pairing can be the dominant pairing channel. The gapless critical state at $x_c\simeq0.25$ has six Dirac points and is topologically nontrivial with a $T^3$ spin relaxation rate below $T_c$.…
Using a recently developed renormalization group method for fermionic superfluids, we determine conditions for d-wave superconductivity in the two-dimensional Hubbard model at moderate interaction strength, and we compute the pairing gap in the superconducting regime. A pairing instability signaled by a divergent flow in the Cooper channel leads to a superconducting state in all studied cases. The next-to-nearest neighbor hopping $t'$ plays a crucial role in the competition between antiferromagnetism and superconductivity. A sizable $t'$ is necessary to obtain a sizable pairing gap.
The ferromagnetism of the checkerboard lattice Hubbard model at quarter filling is one of the few exact ferromagnetic ground states known in the family of Hubbard models. When the nearest neighbor hopping, t1, is negligible compared with the second neighbor one, t2, the system reduces to a collection of Hubbard chains. We find that the 1D character is surprisingly robust as long as t1 < t2. This phenomenon of dimensional reduction due to the geometrical frustration leads to peculiar magnetic orders with 1D character for intermediate U and is responsible for odd-frequency superconducting states…
On the basis of a three orbital model and an effective attractive interaction between electrons we investigate the possible superconducting states, with $p$ and $f$-wave internal symmetry, of Sr$_2$RuO$_4$. For an orbital dependent interaction which acts between in plane and out of plane nearest neighbour Ruthenium atoms we find a state for which the gap in the quasi-particle spectra has a line node on the $α$ and $β$ sheets of the Fermi Surface, but it is complex with no nodes on the $γ$-sheet. We show that this state is consistent with all the available experimental data. In particular, we p…
We implement the rotationally-invariant formulation of the two-dimensional Hubbard model, with nearest-neighbors hopping $t$, which allows for the analytical study of the system in the low-energy limit. Both U(1) and SU(2) gauge transformations are used to factorize the charge and spin contributions to the original electron operator in terms of the corresponding gauge fields. The Hubbard Coulomb energy $U$ term is then expressed in terms of quantum phase variables conjugate to the local charge and variable spin-quantization axis, providing a useful representation of strongly correlated systems…
The two-dimensional Hubbard model exhibits superconductivity with d-wave symmetry even at half-filling in the presence of next-nearest neighbor hopping. Using plaquette cluster dynamical mean-field theory with a continuous-time quantum Monte Carlo impurity solver, we reveal the non-Fermi liquid character of the metallic phase in proximity to the superconducting state. Specifically, the low-frequency scattering rate for momenta near (π, 0) varies non-monotonously at low temperatures, and the dc conductivity is T-linear at elevated temperatures with an upturn upon cooling. Evidence is provided t…
A chiral $p_x+ip_y$ superconductor on a square lattice with nearest and next-nearest hopping and pairing terms is considered. Gap closures, as various parameters of the system are varied, are found analytically and used to identify the topological phases. The phases are characterized by Chern numbers (ranging from -3 to 3), and (numerically) by response to introduction of weak disorder, edges, and magnetic fields in an extreme type-II limit, focusing on the low-energy modes (which presumably become zero-energy Majorana modes for large lattices and separations). Several phases are found, includ…
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 (RPA) spin- and charge-fluctuation approach, and find that while $B_{1g}$ ($d_{x^2-y^2}$) and $B_{2g}$ ($d_{xy}$) pairing dominates in the absence of repulsive longer-range Coulomb interactions $V_{\rm NN}$, the latter induces pairing in other symmetry channels, including e.g $A_{2g}$ ($g$-wave), nodal $A_{1g}$ (e…
It is rigorously shown that the two-dimensional Hubbard model with narrow bands (including next nearest-neighbor hopping, etc.) does not exhibit $d_{x^2 -y^2}$-wave pairing long-range order at any nonzero temperature. This kind of pairing long-range order will also be excluded at zero temperature if an excited energy gap opens in the charge excitation spectrum of the system. These results hold true for both repulsive and attractive Coulomb interactions and for any electron fillings, and are consistent with quantum Monto Carlo calculations.
We investigate the stability domains of ground states of generalized Hubbard models with next-nearest neighbour interaction using the optimum groundstate approach. We focus on the $η$-pairing state with momentum P=0 and the fully polarized ferromagnetic state at half-filling. For these states exact lower bounds for the regions of stability are obtained in the form of inequalities between the interaction parameters. For the model with only nearest neighbour interaction we show that the bounds for the stability regions can be improved by considering larger clusters. Additional next-nearest neigh…
The recent discovery of superconductivity under high pressure in the ladder compound BaFe$_2$S$_3$ has opened a new field of research in iron-based superconductors with focus on quasi one-dimensional geometries. In this publication, using the Density Matrix Renormalization Group technique, we study a two-orbital Hubbard model defined in one dimensional chains. Our main result is the presence of hole binding tendencies at intermediate Hubbard $U$ repulsion and robust Hund coupling $J_H/U=0.25$. Binding does not occur neither in weak coupling nor at very strong coupling. The pair-pair correlatio…
The competition between antiferromagnetism and the $d+id$ superconducting state is studied in a model with near and next near neighbour interactions in the absence of any on-site repulsion. A mean field study shows that it is possible to have simultaneous occurrence of an antiferromagnetic and a singlet $d+id$ superconducting state in this model. In addition, such a coexistence generates a triplet $d+id$ superconducting order parameter with centre of mass momentum $Q=(π, π)$ {\it dynamically} having the same orbital symmetry as the singlet superconductor. Inclusion of next nearest neighbour ho…
Pairing order and condensate fraction across the BCS-BEC crossover in the two-dimensional attractive Hubbard model
Institute of Modern Physics, Northwest University（西北大学现代物理研究所）；School of Physics, Northwest University（西北大学物理学院）；Shaanxi Key Laboratory for Theoretical Physics Frontiers（陕西理论物理前沿重点实验室）；Fundamental Discipline Research Center for Quantum Science and Technology of Shaanxi Province（陕西省量子科学与技术基础学科研究中心）；Hefei National Laboratory（合肥国家实验室）
The Hubbard model and its extensions are important microscopic models for understanding high- $T_c$ superconductivity in cuprates. In the model with next-nearest-neighbor hopping $t'$ (the $t'$- Hubbard model), pairing is strongly influenced by $t'$ . In particular, a recent study on a width-4 cylinder observed quasi-long-rage superconducting order, associated with a negative $t'$ , which was taken to imply superconductivity in the two-dimensional (2D) limit. In this work we study more carefully pairing in the width-4 $t'$-Hubbard model. We show that in this specific system, the pairing symmet…
We use a novel temperature-flow renormalization group technique to analyze magnetic and superconducting instabilities in the two-dimensional t-t' Hubbard model for particle densities close to the van Hove filling as a function of the next-nearest neighbor hopping t'. In the one-loop flow at the van Hove filling, the characteristic temperature for the flow to strong coupling is suppressed drastically around t'_c approx. -0.33t, suggesting a quantum critical point between d-wave pairing at moderate t'>t'_c and ferromagnetism for t'<t'_c. Upon increasing the particle density in the latter regime …
The dynamical density-matrix renormalization group technique is used to calculate spin and charge excitation spectra in the one-dimensional (1D) Hubbard model at quarter filling with nearest-neighbor $t$ and next-nearest-neighbor $t'$ hopping integrals. We consider a case where $t$ ($>0$) is much smaller than $t'$ ($>0$). We find that the spin and charge excitation spectra come from the two nearly independent $t'$-chains and are basically the same as those of the 1D Hubbard (and t-J) chain at quarter filling. However, we find that the hopping integral $t$ plays a crucial role in the short-rang…
We consider an exact solvable interacting spinful Kitaev chain which is a generalization of the Mattis-Nam model. A nearest-neighbor dimerized interaction favoring the production of disjoint molecules drives the quantum phase into an insulating one. The phases are characterized statically and dynamically in terms of magnetization and spin-singlet correlations by using the exact solution. The model is shown to be exactly solvable also in the presence of boundary interactions which are originated from a spin-singlet superconducting pairing and a magnetic field. We exploit the exact solution to i…
The ground state phase diagram of the extended Hubbard model containing nearest and next-to-nearest neighbor interactions is investigated in the thermodynamic limit using an exact method. It is found that taking into account local correlations and adding next-to-nearest neighbor interactions both have significant effects on the position of the phase boundaries. Improved stability domains for the $η$-pairing state and for the fully saturated ferromagnetic state at half filling have been constructed. The results show that these states are the ground states for model Hamiltonians with realistic v…
We investigate the properties of the nearest-neighbor singlet pairing and the emergence of d-wave superconductivity in the doped honeycomb lattice considering the limit of large interactions and the $t-J_1-J_2$ model. First, by applying a renormalized mean-field procedure as well as slave-boson theories which account for the proximity to the Mott insulating state, we confirm the emergence of d-wave superconductivity in agreement with earlier works. We show that a small but finite $J_2$ spin coupling between next-nearest neighbors stabilizes d-wave symmetry compared to the extended s-wave scena…
A two-body problem on the square lattice is analyzed. The interaction potential consists of strong on-site repulsion and nearest-neighbor attraction. Exact pairing conditions are derived for s-, p-, and d-symmetric bound states. The pairing conditions are strong functions of the total pair momentum K. It is found that the stability of pairs increases with K. At weak attraction, the pairs do not form at the $Γ$-point but stabilize at lattice momenta close to the Brillouin zone boundary. The phase boundaries in the momentum space, which separate stable and unstable pairs are calculated. It is fo…
Asymmetric two-leg Hubbard ladders with different on-site interactions $U_y$ and hoppings $t_y$ on each leg are investigated using the density matrix renormalization group method and exact diagonalizations. The pairing found in symmetric ladders is robust against the introduction of the leg asymmetry. When studying pairing, one-band Hubbard ladder models are better described as one-dimensional correlated two-band models than as sublattices of higher dimensional systems. The asymmetric Hubbard ladder provides us with a simple model for studying pairing in the crossover regime between charge tra…
The eta-pairing states are a set of exactly known eigenstates of the Hubbard model on hypercubic lattices, first discovered by Yang [Phys. Rev. Lett. 63, 2144 (1989)]. These states are not many-body scar states in the Hubbard model because they occupy unique symmetry sectors defined by the so-called "eta-pairing SU(2)" symmetry. We study an extended Hubbard model with bond-charge interactions, popularized by Hirsch [Physica C 158, 326 (1989)], where the eta-pairing states survive without the eta-pairing symmetry and become true scar states. We also discuss similarities between the eta-pairing …
Yang's $η$ pairing operator is generalized to explore off-diagonal long-range order in the Hubbard bilayer with an arbitrary chemical potential. With this operator and a constraint condition on annihilation and creation operators, we construct explicitly eigenstates which possess simultaneously three kinds of off-diagonal long-range order, i.e., the intralayer one and the interlayer one for on-site pairing, and that for interlayer nearest-neighbor pairing. As in the simple Hubbard model there is also an SO(4) symmetry, with the the generators properly defined. A sufficient condition leads to a…
We analyze effective d-wave interactions in the two-dimensional extended Hubbard model at weak coupling and small to moderate doping. The interactions are computed from a renormalization group flow. Attractive d-wave interactions are generated via antiferromagnetic spin fluctuations in the pairing and charge channels. Above Van Hove filling, the d-wave charge interaction is maximal at incommensurate diagonal wave vectors, corresponding to nematic fluctuations with a diagonal modulation. Below Van Hove filling a modulation along the crystal axes can be favored. The nematic fluctuations are enha…
The ground state of a one-dimensional Hubbard model having the next-nearest neighbor hopping (t') as well as the nearest-neighbor one (t) is numerically investigated at half-filling. A quantum Monte Carlo result shows a slowly decaying pairing correlation for a sizeable interaction strength $(U \leq 2t)$, while the system is shown to become insulating for yet larger $U>U_C\sim 3t$ from a direct evaluation of the charge gap with the density-matrix renormalization group method. The results are consistent with Fabrizio's recent weak-coupling theory which suggests a transition from a superconducto…
Fully occupied or unoccupied bands in a solid are often considered inert and irrelevant to a material's low-energy properties. But the discovery of enhanced superconductivity in heavily electron-doped FeSe-derived superconductors poses questions about the possible role of incipient bands (those laying close to but not crossing the Fermi level) in pairing. To answer this question, researchers have studied pairing correlations in the bilayer Hubbard model, which has an incipient band for large interlayer hopping $t_\perp$, using many-body perturbation theory and variational methods. They have ge…
