We examine the validity of the weak coupling spin-susceptibility "glue" approximation (SSGA) in a two-dimensional Hubbard model for cuprates. For comparison, we employ the well-established dynamical cluster approximation (DCA) with a quantum Monte Carlo algorithm as a cluster solver. We compare the leading eigenvalues and corresponding eigenfunctions of the DCA and SSGA pairing matrices. For realistic model parameters, we find that the SSGA fails to capture the leading pairing symmetries seen in the DCA. Furthermore, when the SSGA is improved through the addition of a term with d-wave symmetry, the strength of this additional term is found to be larger than that of the "glue" approximation.
The question of whether one should speak of a "pairing glue" in the Hubbard and t-J models is basically a question about the dynamics of the pairing interaction. If the dynamics of the pairing interaction arises from virtual states, whose energies correspond to the Mott gap, and give rise to the exchange coupling J, the interaction is instantaneous on the relative time scales of interest. In this case, while one might speak of an "instantaneous glue", this interaction differs from the traditional picture of a retarded pairing interaction. However, if the energies correspond to the spectrum see…
The two-layer Hubbard model is studied by using the composite operator method. Magnetic properties of the model in the normal state are analyzed by studying the uniform static spin magnetic susceptibility as a function of doping and temperature. The relevance of the model to describe the physical behavior of two-layered cuprate high-$T_{c}$ superconductors is discussed.
A dynamic cluster quantum Monte Carlo algorithm is used to study a spin susceptibility representation of the pairing interaction for the two-dimensional Hubbard model with an on-site Coulomb interaction equal to the bandwidth for various doping levels. We find that the pairing interaction is well approximated by ${3/2}\Ub(T)^2χ(K-K')$ with an effective temperature and doping dependent coupling $\Ub(T)$ and the numerically calculated spin susceptibility $χ(K-K')$. We show that at low temperatures, $\Ub$ may be accurately determined from a corresponding spin susceptibility based calculation of t…
It has gone almost unquestioned that superexchange in the t-J (or Hubbard) model, and not phonons, is responsible for the unconventional ("d-wave") pairing symmetry of cuprate superconductors. However a number of advanced numerical studies have not found superconductivity in the Hubbard model. On the other hand compelling experimental evidence for a strong electron-phonon interaction (EPI) has currently arrived. Here I briefly review some phonon-mediated unconventional pairing mechanisms. In particular the anisotropy of sound velocity makes the phonon-mediated attraction of electrons non-local…
Using the Dynamical Cluster Approximation (DCA) we calculate the alternating circulating-current susceptibility and investigate the transition to the d-density wave (DDW) order in the two-dimensional Hubbard model. The 2 x 2 cluster used in the DCA calculation is the smallest that can capture d-wave order; therefore, due to the mean-field character of our calculation, we expect to overestimate d-wave transition temperatures. Despite this, we found no transition to the DDW state. In the pseudogap region the DDW susceptibility is enhanced, as predicted by the slave boson SU(2) theory, but it sti…
Using numerical dynamic cluster quantum Monte Carlo results, we study a simple approximation for the pairing interaction of a two-dimensional Hubbard model with an on-site Coulomb interaction $U$ equal to the bandwidth. We find that with an effective temperature dependent coupling $\Ub(T)$ and the numerically calculated spin susceptibility $χ(K-K')$, the d-wave pairing interaction is well approximated by $\frac{3}{2} \Ub^2χ(K-K')$.
At temperatures above the superconducting transition temperature the pairfield susceptibility provides information on the nature of the pairfield fluctuations. Here we study the d-wave pairfield susceptibility of a 2D Hubbard model for dopings which have a pseudogap (PG) and for dopings which do not. One knows that in both cases there will be a region of Kosterlitz-Thouless fluctuations as the transition at $T_{KT}$ is approached. Above this region we find evidence for Emery-Kivelson phase fluctuations for dopings with a PG and Gaussian amplitude fluctuations for dopings without a PG.
The spin-rotationally invariant SU(2) approach to the Hubbard model is extended to accommodate the charge degrees of freedom. Both U(1) and SU(2) gauge transformation are useed to factorize the charge and spin contribution to the original electron operator in terms of the emergent gauge fields. It is shown that these fields play a similar role as phonons in the BCS theory: they provide the "glue" for fermion pairing. By tracing out gauge bosons the form of paired states is established and the role of antiferromagnetic correlations is explicated.
We present an approach for determining susceptibilities and order parameters in multi-band Hubbard model within functional renormalization group method, and apply it to study various instabilities of the FeAs-based high temperature superconductor. First, we derive the formulae of susceptibilities and order parameters of superconducting parings, spin density waves and charge density waves with diverse wave vectors which could occur in multi-band Hubbard model. Second, we apply it to the FeAs-based high temperature superconductor and find an electronic-driven superconducting pairing instability …
Nematic order resulting from the partial melting of density-waves has been proposed as the mechanism to explain nematicity in iron-based superconductors. An outstanding question, however, is whether the microscopic electronic model for these systems -- the multi-orbital Hubbard model -- displays such an ordered state as its leading instability. In contrast to usual electronic instabilities, such as magnetic and charge order, this fluctuation-driven phenomenon cannot be captured by the standard RPA method. Here, by including fluctuations beyond RPA in the multi-orbital Hubbard model, we derive …
We study the contribution of the electron-spin fluctuation coupling to the superconducting state of the two dimensional Hubbard model within dynamical cluster approximation (DCA) using a numerical exact continuous time Monte Carlo solver. By analyzing the frequency dependence of the self energy, we show that only about half of the superconductivity can be attributed to a "pairing glue" arising from treating spin fluctuations as a pairing boson in the standard one-loop theory.
We study the occurrence and the origin of ferromagnetic fluctuations in the longitudinal spin susceptibility of the $t$-$t'$-Rashba-Hubbard model on the square lattice. The combined effect of the second-neighbor hopping $t'$ and the spin-orbit coupling leads to ferromagnetic fluctuations in a broad filling region. The spin-orbit coupling splits the energy bands, leading to two van Hove fillings, where the sheets of the Fermi surface change their topology. Between these two van Hove fillings the model shows ferromagnetic fluctuations. We find that these ferromagnetic fluctuations originate from…
Effects of electron correlation on the Fermi surface is investigated for the two-dimensional Hubbard model by the quantum Monte Carlo method. At first, an infinitesimal doping from the half filling is focused on and the momentum dependent charge susceptibility $κ(k)=\frac {dn(k)}{dμ}$ is calculated at a finite temperature. At the temperature $T \sim \frac {t^2} U$, it shows peak structure at $(\pm π/2,\pm π/2)$ on the Fermi surface (line). It is consistent with the mean-field prediction of the d-wave pairing state or the staggerd flux state. This momentum dependent structure disappears at the …
We propose theoretically that a magnetic field can realize spin-triplet superconductivity in repulsively interacting electron systems having strong ferromagnetic spin fluctuations. We confirm the general idea for the low-density Hubbard model on a triangular lattice, whose Fermi surface consists of disconnected pieces, by calculating the pairing susceptibility in a moderate magnetic field with the quantum Monte-Carlo method combined with the dynamical cluster approximation.
We study the two-dimensional Hubbard model with nonmagnetic Zn impurities modeled by binary diagonal disorder using Quantum Monte Carlo within the Dynamical Cluster Approximation. With increasing Zn content we find a strong suppression of d-wave superconductivity concomitant to a reduction of antiferromagnetic spin fluctuations. $T_c$ vanishes linearly with Zn impurity concentration. The spin susceptibility changes from pseudogap to Curie-Weiss like behavior indicating the existence of free magnetic moments in the Zn doped system. We interpret these results within the RVB picture.
We study the fluctuations responsible for pairing in the $d$-wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity solver. By analyzing how momentum and frequency dependent fluctuations generate the $d-$wave superconducting state in different representations, we identify antiferromagnetic fluctuations as the pairing glue of superconductivity both in the underdoped and the overdoped regime. Nevertheless, in the intermediate coupling regime, the predominant magnetic fluctuati…
We calculate the charge compressibility and uniform spin susceptibility for the two-dimensional (2D) Hubbard model slightly away from half-filling within a two-loop renormalization group scheme. We find numerically that both those quantities flow to zero as we increase the initial interaction strength from weak to intermediate couplings. This result implies gap openings in both charge and spin excitation spectra for the latter interaction regime. When this occurs, the ground state of the lightly doped 2D Hubbard model may be interpreted as an insulating spin liquid as opposed to a Mott insulat…
We study, within the fluctuation exchange approximation, the spin-fluctuation-mediated superconductivity in Hubbard-type models possessing electron and hole bands, and compare them with a model on a square lattice with a large Fermi surface. In the square lattice model, superconductivity is more enhanced for better nesting for a fixed band filling. By contrast, in the models with electron and hole bands, superconductivity is optimized when the Fermi surface nesting is degraded to some extent, where finite energy spin fluctuation around the nesting vector develops. The difference lies in the ro…
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…
Dynamic cluster Monte Carlo calculations for the doped two-dimensional Hubbard model are used to study the irreducible particle-particle vertex responsible for $d_{x^2-y^2}$ pairing in this model. This vertex increases with increasing momentum transfer and decreases when the energy transfer exceeds a scale associated with the $Q=(π, π)$ spin susceptibility. Using an exact decomposition of this vertex into a fully irreducible two-fermion vertex and charge and magnetic exchange channels, the dominant part of the effective pairing interaction is found to come from the magnetic, spin S=1 exchange …
Recent observation of a "kink" in single-particle dispersion in photoemission experiments on cuprate superconductors has initiated a heated debate over the issue of a boson that mediates the pairing in cuprates. If the "kink" is indeed caused by interaction with a bosonic excitation, then there are two possible candidates: phonons and spin fluctuations. Here, the role of anti-ferromagnetic spin fluctuations in shaping the phase diagram of cuprate superconductors will be discussed. By using the local (momentum-integrated) dynamic spin susceptibility, recently measured in neutron scattering expe…
Two-particle (2-p) excitations such as spin and charge excitations play a key role in high-Tc cuprate superconductors (HTSC). On the basis of a parameter-free theory, which extends the Variational Cluster Approach (a recently developed embedded cluster method) to 2-p excitations, the magnetic excitations of HTSC are shown to be reproduced for a Hubbard model within the relevant strong-coupling regime. In particular, the resonance mode in the underdoped regime, its intensity and "hour-glass" dispersion are in good overall agreement with experiments.
We use the dynamical cluster approximation to understand the proximity of the superconducting dome to the quantum critical point in the two-dimensional Hubbard model. In a BCS formalism, $T_c$ may be enhanced through an increase in the d-wave pairing interaction ($V_d$) or the bare pairing susceptibility ($χ_{0d}$). At optimal doping, where $V_d$ is revealed to be featureless, we find a power-law behavior of $χ_{0d}(ω=0)$, replacing the BCS log, and strongly enhanced $T_c$. We suggest experiments to verify our predictions.
Monte Carlo calculations of the irreducible particle-particle interaction on a two-leg Hubbard ladder doped near half-filling are reported. As the temperature is lowered, this interaction develops structure in momentum space similar to the magnetic susceptibility $χ(q)$ and reflects the development of strong short-range antiferromagnetic correlations. Using this interaction, the eigenfunction of the leading singlet pair eigenvalue is found to have $d_{x^2-y^2}$ like symmetry. The single-particle spectral weight is also shown to peak near $(π,0)$ and $(0,π)$ when the ratio of the inter- to intr…
The dual-fermion approach offers a way to perform diagrammatic expansion around the dynamical mean-field theory. Using this formalism, the influence of antiferromagnetic fluctuations on the self-energy is taken into account through ladder-type diagrams in the particle-hole channel. The resulting phase diagram for the (quasi-)two-dimensional Hubbard model exhibits antiferromagnetism and d-wave superconductivity. Furthermore, a uniform charge instability, i.e., phase separation, is obtained in the low doping regime around the Mott insulator. We also examine spin/charge density wave fluctuations …
Using the dynamical cluster approximation, we calculate the correlation functions associated with the nearest neighbor bond operator which measure the z component of the spin exchange in the two-dimensional Hubbard model with $U$ equal to the bandwidth. We find that in the pseudogap region, the local bond susceptibility diverges at T=0. This shows the existence of degenerate bond spin excitation and implies quantum criticality and bond order formation when long range correlations are considered. The strong correlation between excitations on parallel neighboring bonds suggests bond singlet dime…
To understand nontrivial edge electronic states in strongly-correlated metals such as cuprate superconductors, we study the two-dimensional Hubbard models with open edge boundary. The position-dependences of the spin susceptibility and the self-energy are carefully analyzed self-consistently, by using the fluctuation-exchange (FLEX) approximation. It is found that spin susceptibilities are strongly enlarged near the (1,1) open edge when the system is near the half-filling. The enhancement is large even if the negative feedback from the self-energy is considered in the FLEX approximation. The p…
The two-dimensional Holstein-Hubbard model is studied by means of continuous-time quantum Monte Carlo simulations. Using renormalization-group-invariant correlation ratios and finite-size extrapolation, the critical temperature of the charge-density-wave transition is determined as a function of coupling strength, phonon frequency, and Hubbard repulsion. The phase transition is demonstrated to be in the universality class of the two-dimensional Ising model and detectable via the fidelity susceptibility. The structure of the ground-state phase diagram and the possibility of a bipolaronic metal …
We report on the result of quantum Monte Carlo simulation of quasi-one-dimensional electron systems at 1/4-filling, considering organic superconductors such as TMTSF- and TMTTF-salts. We focus on the effect of dimensionality (interchain coupling) on superconducting fluctuation. First we consider Hubbard model which includes only on-site repulsion U. We find that the increase of interchain coupling enhances superconducting susceptibility, although it deforms the nested Fermi surface and suppresses the spin susceptibility. Next we consider an extended Hubbard model which includes nearest-neighbo…
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 …
Evidence for the presence of high energy magnetic excitations in overdoped La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) has raised questions regarding the role of spin-fluctuations in the pairing mechanism. If they remain present in overdoped LSCO, why does $T_c$ decrease in this doping regime? Here, using results for the dynamic spin susceptibility ${\rm Im}χ(q,ω)$ obtained from a determinantal quantum Monte Carlo (DQMC) calculation for the Hubbard model we address this question. We find that while high energy magnetic excitations persist in the overdoped regime, they lack the momentum to scatter pairs bet…
We study the three-band Hubbard model for the copper oxide plane of the high-temperature superconducting cuprates using determinant quantum Monte Carlo and the dynamical cluster approximation (DCA) and provide a comprehensive view of the pairing correlations in this model using these methods. Specifically, we compute the pair-field susceptibility and study its dependence on temperature, doping, interaction strength, and charge-transfer energy. Using the DCA, we also solve the Bethe-Salpeter equation for the two-particle Green's function in the particle-particle channel to determine the transit…
We investigate the Bose glass phase and the insulator-to-superfluid transition in the two-dimensional disordered boson Hubbard model in the Villain representation via Monte Carlo simulations. In the Bose glass phase the probability distribution of the local susceptibility is found to have a $1/ χ^2$ tail and the imaginary time Green's function decays algebraically $C(τ) \sim τ^{-1}$, giving rise to a divergent global susceptibility. By considering the participation ratio it is shown that the excitations in the Bose glass phase are fully localized and a scaling law is established. For commensur…
We investigate the mapping between magnetic susceptibility and entanglement in the metallic, insulating, conventional and exotic polarized superfluid phases of one-dimensional fermionic lattice systems as described by the Hubbard model. Motivated by recent proposals for determining and quantifying entanglement via magnetic susceptibility measurements, we numerically study the intrinsic relationship between the two quantities at zero temperature. We find signatures of the metal-insulator transition and of the BCS-BEC crossover, but the most relevant result is that for conventional and exotic su…
We study the Villain representation of the two-dimensional disordered boson Hubbard model via Monte Carlo simulations. It is shown that the probability distribution of the local susceptibility has a 1/χ^2-tail in the Bose glass phase. This gives rise to a divergence although particles are completely localized here as we prove with the help of the participation ratio. We demonstrate the presence of an incompressible Mott lobe within the Bose glass phase and show that a direct Mott-insulator to superfluid transition happens at the tip of the lobe. Here we find critical exponents z=1, ν~0.7$ and …
Motivated by the presence of an extremely small electron pocket in the electronic band structure of infinite-layer (IL) nickelate superconductors, we systematically explore the superconducting (SC) properties of a two-dimensional Hubbard model influenced by an additional conduction band with small occupancy (dry Fermi sea). Our dynamic cluster quantum Monte Carlo calculations demonstrated the unusual impact of this additional dry metallic layer, which shifts the SC dome of the correlated Hubbard layer towards the overdoped regime, namely the $d$-wave SC can be enhanced (suppressed) in the over…
