Quantum Simulation of the Hubbard Model: The Attractive Route
A. F. Ho, M. A. Cazalilla, T. Giamarchi
备注：
11 pages, 5 figs. New version as accepted in PRA. We have clarified the models we are discussing in various places, and expanded on the critical number estimate to include both K40 and Li6 in section V. Also added references
We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely a Mott insulator in the paramagnetic and anti-ferromagnetic phases, and a putative d-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultra-cold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We show that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are in fact more easy to observe as a paired, and superfluid phase respectively, in the attractive Hubbard model. The putative d-wave superfluid phase of the repulsive Hubbard model doped away from half-filling is related to a d-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to 'quantum simulate' the Hubbard model in an optical lattice over the approach that attempts to directly simulate the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.
We investigate the competition between superconductivity (SC) and charge density wave (CDW) under a time-dependent periodic field in the attractive Hubbard model. By employing the time-dependent exact diagonalization method, we show that the driving frequency and amplitude of the external field can control the enhancement of either the superconducting pair or the CDW correlations, which are degenerate in the ground state of the half-filled attractive Hubbard model in the absence of the field. In the strong-coupling limit of the attractive Hubbard interaction, the controllability is characteriz…
We study the superconducting Kosterlitz-Thouless transition of the attractive Hubbard model on a two-dimensional triangular lattice using auxiliary field quantum Monte Carlo method for system sizes up to $12\times 12$ sites. Combining three methods to analyze the numerical data, we find, for the attractive interaction of $U=-4t$, that the transition temperature stays almost constant within the band filling range of $1.0 < n < 1.4$, while it is found to be much lower in the $n<1$ region.
We solve the attractive Hubbard model for arbitrary interaction strengths within dynamical mean-field theory. We compute the transition temperature for superconductivity and analyze electron pairing in the normal phase. The normal state is a Fermi liquid at weak coupling and a non-Fermi liquid state with a spin gap at strong coupling. Away from half-filling, the quasi-particle weight vanishes discontinuously at the transition between the two normal states.
Angle-resolved photoemission spectra are calculated microscopically for the two-dimensional attractive Hubbard model. A system of self-consistent T-matrix equations are solved numerically in the real-time domain. The single-particle spectral function has a two-peak structure resulting from the presense of bound states. The spectral function is suppressed at the chemical potential, leading to a pseudogap-like behavior. At high temperatures and densities the pseudogap diminishes and finally disappears; these findings are similar to experimental observations for the cuprates.
We investigate spontaneously symmetry breaking states in the attractive SU($N$) Hubbard model at half filling. Combining dynamical mean-field theory with the continuous-time quantum Monte Carlo method, we obtain the finite temperature phase diagrams for the superfluid state. When $N>2$, the second-order phase transition occurs in the weak coupling region, while the first-order phase transition with the hysteresis appears in the strong coupling region. We also discuss the stability of the density wave state and clarify the component dependence of the maximum critical temperature.
The coexistence of superconducting and charge-density-wave order in the half-filled attractive Hubbard model is interpreted as a consequence of the pseudospin SU(2) symmetry spontaneously broken to a `hidden' subgroup U(1). By topological arguments we show that there must exist new skyrmion textures associated with this symmetry breakdown. This fact is illustrated via a non-linear $σ$-model. Unlike the spin textures previously known in an antiferromagnetic background, doping the model away from half-filling leads the new skyrmions to unwrap.
We contrast the transport properties (dc resistivity, Seebeck coefficient), optical conductivity, spectral functions, dynamical magnetic susceptibility, and the NMR $1/T_1$ spin-lattice relaxation rate of the repulsive and attractive infinite-dimensional Hubbard models in the paramagnetic phase for a generic band filling. The calculations are performed in a wide temperature interval using the dynamical mean-field theory with the numerical renormalization group as the impurity solver. The attractive case exhibits significantly more complex temperature dependences which can be explained by the b…
We investigate the electronic and superconducting properties of a negative-U Hubbard model. For this purpose we evaluate a recently introduced variational theory based on Gutzwiller-correlated BCS wave functions. We find significant differences between our approach and standard BCS theory, especially for the superconducting gap. For small values of $|U|$, we derive analytical expressions for the order parameter and the superconducting gap which we compare to exact results from perturbation theory.
We discuss the phase diagram of the extended Hubbard model with both attractive and repulsive local and nonlocal interactions. The extended dynamical mean-field theory (EDMFT) and the dual boson method (DB) are compared. The latter contains additional nonlocal correlation effects that are not incorporated in EDMFT. We find that EDMFT and DB give almost identical results in the attractive $V$ regime, where phase separation occurs. This is quite a difference with the previously studied repulsive $V$ regime, where EDMFT and DB give very different phase boundaries for the checkerboard order phase,…
We analyze the normal phase of the attractive Hubbard model within dynamical mean-field-theory. We present results for the pair-density, the spin-susceptibility, the specific heat, the momentum distribution, and for the quasiparticle weight. At weak coupling the low-temperature behavior of all quantities is consistent with Fermi liquid theory. At strong coupling all electrons are bound pairs, which leads to a spin gap and removes fermionic quasi-particle excitations. The transition between the Fermi liquid phase and the pair phase takes place at a critical coupling of the order of the band-wid…
Fermi gases and liquids display an excitation spectrum that is simply connected, ensuring closed Fermi surfaces. In strongly correlated systems like the cuprate superconductors, the existence of open sheets of Fermi surface known as Fermi arcs indicates a distinctly different topology of the spectrum with no equivalent in Fermi liquid theory. Here, we demonstrate a generic mechanism by which correlation effects in fermionic systems can change the topology of the spectrum. Using diagrammatic Monte Carlo simulations, we demonstrate the existence of disconnected and multiply connected excitation …
Ultracold atoms in optical lattice provides a platform to realize the superfluid (SF) state, a quantum order with paired charge-neutral fermions. In this paper, we studied SF state in the twodimensional attractive Hubbard model with pi-flux on each plaquette. The SF state in the pi-flux lattice model suffers very strong quantum fluctuations and the ground state becomes a possible quantum phase liquid state. In this phase, there exists the Cooper pairing together with a finite energy gap for the atoms, but no long range SF phase coherence exists at zero temperature. In addition, we discussed th…
The extended Hubbard model with an attractive density-density interaction, positive pair hopping, or both, is shown to host topological phases, with a doubly degenerate entanglement spectrum and interacting edge spins. This constitutes a novel instance of topological order which emerges from interactions. When the interaction terms combine in a charge-SU(2) symmetric fashion, a novel partially polarized pseudospin phase appears, in which the topological features of the spin degrees of freedom coexist with long-range $η$-wave superconductivity. Thus, our system provides an example of an interpl…
Attractive interaction between fermions can lead to pairing and superfluidity in an optical lattice. In contrast to the `continuum', on a lattice the trap induced density variation can generate a non monotonic profile of the pairing amplitude, and completely modify the spectral signatures of any possible pseudogap phase. Using a tool that fully captures the inhomogeneity and strong thermal fluctuations, we demonstrate how the crucial radio frequency signatures of pairing are `inverted' in a trapped attractive fermion lattice compared to the traditional continuum case. These features would be c…
We calculate the one-electron spectral function of the attractive-U Hubbard model in two dimensions. We work in the intermediate coupling and low density regime and evaluate analytically the self-energy. The results are obtained in a framework based on the self-consistent T-matrix approximation. We also calculate the chemical potential of the bound pairs as a function of temperature. On the basis of this calculation we analyze the low-temperature resistivity and specific heat in the normal state of this system. We compare our results with recent beautiful tunneling experiments in the underdope…
The ground-state properties of the Hubbard model with attractive local pairing interactions are investigated in the framework of lattice density-functional theory. A remarkable correlation is revealed between the interaction-energy functional $W[\boldsymbolη]$ corresponding to the Bloch-state occupation-number distribution $η_{\boldsymbol{k}σ}$ and the entropy $S[\boldsymbolη]$ of a system of non-interacting fermions having the same $η_{\boldsymbol{k}σ}$. The relation between $W[\boldsymbolη]$ and $S[\boldsymbolη]$ is shown to be approximately linear for a wide range of ground-state representa…
The ground state phase diagram of the two-dimensional attractive Hubbard model with population imbalance is explored using a mean field ansatz. A linear programming algorithm is used to identify the blocked states, such that the population imbalance can be imposed exactly. This allows to explore regions of the number-projected phase diagram that can not be obtained with the conventional Bogoliubov-de Gennes ansatz. The Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase of pairs with non-zero momentum is found to be the ground state over a wide range of parameters, while phase separation occurs only …
We investigate low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction U < 0 using the density matrix renormalization group method as well as a perturbation theory. We find that the ground state is a charge density wave state with a long range order. The ground state is completely incompressible since all the excitations are gapful. The charge gap which is the same as the four-particle excitation gap is a non-monotonic function of U, while the spin gap and others increase with increasing |U| and have linear asymptotic behaviors.
In this work, we adapt the formalism of the dynamical vertex approximation (D$Γ$A), a diagrammatic approach including many-body correlations beyond the dynamical mean-field theory, to the case of attractive onsite interactions. We start by exploiting the ladder approximation of the D$Γ$A scheme, in order to derive the corresponding equations for the non-local self-energy and vertex functions of the attractive Hubbard model. Second, we prove the validity of our derivation by showing that the results obtained in the particle-hole symmetric case fully preserve the exact mapping between the attrac…
In this review paper, we illustrate a possible route to obtain a reliable solution of the 2D Hubbard model and an explanation for some of the unconventional behaviours of underdoped high-$T_\text{c}$ cuprate superconductors within the framework of the composite operator method. The latter is described exhaustively in its fundamental philosophy, various ingredients and robust machinery to clarify the reasons behind its successful applications to many diverse strongly correlated systems, controversial phenomenologies and puzzling materials.
In this work, a two-dimensional one-band Hubbard model is investigated within a two-pole approximation. The model presents a non-local attractive potential $U (U<0)$ that allows the study of d-wave superconductivity and also includes hopping up to second-nearest-neighbors. The two-pole scheme has been proposed to improve the Hubbard-I approximation. The analytical results show a more complex form for the gap $Δ(T)$, when compared to the one obtained in the latter approximation. Indeed, new anomalous correlation functions associated with the superconductivity are involved in the calculation of …
We derive an efficient method for treating renormalization contributions at two-loop level within the functional renormalization group in the one-particle irreducible formalism for fermions. It is based on a decomposition of the two-particle vertex in charge, magnetic and pairing channels. The method treats single-particle and collective excitations in all channels on equal footing, allows for the description of symmetry-breaking and captures collective mode fluctuation physics in the infrared. As a first application, we study the superfluid ground state of the two-dimensional attractive Hubba…
The paramagnetic phase of the extended attractive Hubbard model on the cubic lattice is studied within the spin rotation invariant Kotliar-Ruckenstein slave-boson representation at zero temperature. It is obtained that the quasiparticle residue of the Fermi liquid phase vanishes for all densities at an interaction strength slightly smaller than $U_c$ that signals the Brinkman-Rice transition, and that it weakly depends on density. While for vanishing non-local interaction parameters homogeneous static charge instabilities are found in a rather narrow window centered around quarter filling and …
A Fermi liquid with weak attractive interaction undergoes a BCS transition to a superconductor with reducing temperature. With increasing interaction strength, the thermal transition is progressively modified as the high temperature `metallic' phase develops a pseudogap due to pairing fluctuations and the resistivity above T_c shows insulating behaviour. The crossover to insulating character occurs much before the system can be considered to be in the BEC regime of preformed fermion pairs. We use a new Monte Carlo tool to map out the BCS-BEC crossover in the attractive Hubbard model on large t…
We study a one-dimensional SU(N) Hubbard model with an attractive on-site interaction and $N>2$ at half-filling on the bipartite lattice using density-matrix renormalization-group method and a perturbation theory. We find that the ground state of the SU(N) Hubbard model is a charge density wave state with two-fold degeneracy. All the excitations are found to be gapful, resulting in an insulating ground state, on contrary to that in the SU(2) case. Moreover, the charge gap is equal to the Cooperon gap, which behaves as $-2Nt^2/(N-1)U$ in the strong coupling regime. However, the spin gap $Δ_{s}$…
Extending the U(1) slave-rotor representation\cite{FG_SRR} of the repulsive Hubbard model, we propose an SU(2) slave-rotor decomposition for the attractive Hubbard model, where the SU(2) slave-rotor variables represent order parameter fluctuations associated with superconductivity and charge density wave. This decomposition method allows us to modify the standard Hartree-Fock mean field theory by incorporating order parameter fluctuations on an equal footing. Deriving an effective SU(2) slave-rotor action from the attractive Hubbard model, and analyzing it at the mean field level, we demonstra…
We explore the pairing properties of the one-dimensional attractive Hubbard model in the presence of finite spin polarization. The correlation exponents for the most important fluctuations are determined as a function of the density and the polarization. We find that in a system with spin population imbalance, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-type pairing at wavevector Q=|k_{F,\uparrow}-k_{F,\downarrow}| is always dominant and there is no Chandrasekhar-Clogston limit. We then investigate the case of weakly coupled 1D systems and determine the region of stability of the 1D FFLO phase. Th…
Using the Dyson equation of motion for both the diagonal one-particle Green function, $G(\vec{k},ω)$ and off--diagonal Green function, $F(\vec{k},ω)$, at the level of the Hubbard--I decoupling scheme, we have found that they have four poles symmetric in pairs, justifying a more elaborated calculation done by the Zürich group by means of the $T$-Matrix approach (Pedersen et al, Z. Physik B {\bf 103}, 21 (1997)) and the moment approach of Nolting (Z. Physik {\bf 255}, 25 (1972)). We find that the energy spectra and the weights of $G(\vec{k},ω)$ and $F(\vec{k},ω)$ have to be calculated self-consi…
Recent experimental discovery of several families of kagome-lattice materials has boosted the interest in electronic correlations on kagome lattice. As an initial step to understand the observed complex phenomena, it is helpful to know the correspondence between simple forms of interactions and the induced correlated states on kagome lattice. Considering the lack of such studies, here we systematically investigate the attractive kagome-lattice Hubbard model using the mean-field approach and determinant quantum Monte Carlo (DQMC). A charge-density-wave order satisfying the triangle rule is pred…
In this Rapid Communication we show that low energy macroscopic properties of the one-dimensional (1D) attractive Hubbard model exhibit two fluids of bound pairs and of unpaired fermions. Using the thermodynamic Bethe ansatz equations of the model, we first determine the low temperature phase diagram and analytically calculate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing correlation function for the partially-polarized phase. We then show that for such a FFLO-like state in the low density regime the effective chemical potentials of bound pairs and unpaired fermions behave like two free …
We study the percolative superconducting transition as the density of randomly placed attractive centers grows in a host metal. Employing the Hubbard-Stratanovich transformation for the interaction and allowing for spatial, thermal fluctuations of the pairing field, we obtain real-space features of the transition from weak to strong coupling. Spectral and transport properties are studied in detail. BCS-BEC crossover is discussed in the context of site dilution of attractive centers.
Pseudogap formation in the moderate correlated layered attractive Hubbard model
Russian Quantum Center（俄罗斯量子中心）；National University of Science and Technology “MISIS”（莫斯科国立科技大学 MISIS）；Department of Physics, National Research University Higher School of Economics（高等经济大学物理系）；Lomonosov Moscow State University（莫斯科国立罗蒙诺索夫大学）；London School of Economics and Political Science（伦敦政治经济学院）
Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility---ultimately signalling charge instability and phase separation---and its correlation induced suppression. We analyse this scenario through the investigation of the extended Hubbard model on a two-dimensional square lattice, using the spin rotation invariant slave-boson representation of Kotliar and Ruckenstein. The quasiparticle density of states, the renormalised effective mass and t…
Some exact results are given, that connect, for a general magnitude of the interaction term $U$, the repulsive and attractive Hubbard model, in terms of the eigenspectra and quantum diffusion properties. In particular, it is shown that, for some initial conditions, the quantum evolution cannot differenciate between the attractive and repulsive models. These results apply to both fermionic and bosonic models, in any dimension and for general filling, as far as the underlying structure is bipartite.
We study the two-dimensional attractive Hubbard model using the mapping onto the half-filled repulsive Hubbard model in a uniform magnetic field coupled to the fermion spins. The low-energy effective action for charge and pairing fluctuations is obtained in the hydrodynamic regime. We recover the action of a Bose superfluid where half the fermion density is identified as the conjugate variable of the phase of the superconducting order parameter. By integrating out charge fluctuations, we obtain a phase-only action. In the zero-temperature superconducting state, this action describes a collecti…
Using the negative U Hubbard model we analyze normal state properties of a superconductor. In this model there exists a characteristic pairing temperature T_P above a superconducting critical temperature. Below T_P electrons start to form incoherent pairs. The fluctuations in charge and phase are precursors of charge density wave and superconductivity phases depending on band filling. They lead naturally to pseudogap opening in the density of states.
Experiments on polarized fermion gases performed by trapping ultracold atoms in optical lattices, allow the study of an attractive Hubbard model for which the strength of the on site interaction is tuned by means of a Feshbach resonance. Using a well-known particle-hole transformation we discuss how results obtained for this system can be reinterpreted in the context of a doped repulsive Hubbard model. In particular we show that the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state corresponds to the striped state of the two-dimensional doped positive U Hubbard model. We then use the results of nu…
In this paper, we study the effects of attractive correlation on the topological insulator ($TI$) with topological flat-bands using an extended attractive Kane-Mele-Hubbard model (KMHM). In the KMHM, we found a quantum phase transition from $TI$ to the superconductor ($SC$) state upon the increasing of the attractive Hubbard interaction $U$ at the mean field level. This type of $SC$ phase transition is different from the traditional $SC$ phase transition which develops from the gapless Fermi Liquid. Cooperon-type gapped excitations exist in the $TI$ side near this type of $SC$ phase transition…
We present an effective Hamiltonian based real-space approach for studying the weak-coupling Bardeen-Cooper-Schrieffer (BCS) to the strong-coupling Bose-Einstein condensate (BEC) crossover in the two-dimensional attractive Hubbard model at finite temperatures. We introduce and justify an effective classical Hamiltonian to describe the thermal fluctuations of the relevant auxiliary fields. Our results for $T_c$ and phase diagrams compare very well with those obtained from more sophisticated and {\it cpu}-intensive numerical methods. We demonstrate that the method works in the presence of disord…
In this review we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. Main emphasis is made on recent developments which include results for both spin and electron flat-band models. In particular, for flat-band spin systems we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat band due to nonideal lattice geometry. For electronic systems, we discuss the universal low-temper…
We investigate the possibility of unconventional spin density wave (SDW) in the attractive Hubbard model with finite spin polarization. We show that pairing and density fluctuations induce the transverse d-wave SDW near the half-filling. This novel SDW is related to the d-wave superfluidity induced by antiferromagnetic spin fluctuations, in the sense that they are connected with each other through Shiba's attraction-repulsion transformation. Our results predict the d-wave SDW in real systems, such as cold Fermi atom gases with population imbalance and compounds involving valence skipper elemen…
The superfluid properties of the attractive Hubbard model in a Zeeman magnetic field, and in the weak coupling regime have been investigated. The temperature and magnetic field dependencies of the order parameter have been analyzed. Furthermore, the temperature vs. magnetic field and temperature vs. spin polarization phase diagrams for the 2D and 3D lattices have been obtained. For some parameters a reentrant transition has been found.
We have applied the Fast Fourier transform (FFT), which allows to compute efficiently convolution sums, to solve the set of self-consistent T-matrix equations to get the Green function of the two dimensional attractive-U Hubbard modelbelow $T_c$, extending previous calculations of the same authors. Using a constant order parameter $Δ(T)$, we calculated $T_c$ as a function of electron density and interaction strength $U$. These global results deviate from the BCS behavior remarkably.
Pump-probe experiments have turned out as a powerful tool in order to study the dynamics of competing orders in a large variety of materials. The corresponding analysis of the data often relies on standard linear-response theory generalized to non-equilibrium situations. Here we examine the validity of such an approach within the attractive Hubbard model for which the dynamics of pairing and charge-density wave orders is computed using the time-dependent Hartree-Fock approximation (TDHF). Our calculations reveal that the `linear-response assumption' is justified for small to moderate non-equil…
We investigate the competition between superconductivity, charge-ordering, magnetic-ordering, and the Kondo effect in a heavy fermion $s$-wave superconductor described by a Kondo lattice model with an attractive on-site Hubbard interaction. The model is solved using the real-space dynamical mean field theory. For this purpose, we develop a numerical renormalization group (NRG) framework in Nambu space, which is used to solve the superconducting impurity problem. This extended NRG scheme also allows for SU(2) spin symmetry broken solutions, enabling us to examine the competition or cooperation …
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）
We study the long-distance asymptotic behavior of various correlation functions for the one-dimensional (1D) attractive Hubbard model in a partially polarized phase through the Bethe ansatz and conformal field theory approaches. We particularly find the oscillating behavior of these correlation functions with spatial power-law decay, of which the pair (spin) correlation function oscillates with a frequency $Δk_F$ ($2Δk_F$). Here $Δk_F=π(n_\uparrow-n_\downarrow)$ is the mismatch in the Fermi surfaces of spin-up and spin-down particles. Consequently, the pair correlation function in momentum spa…
Superfluidity without charge order in the attractive Hubbard model on the kagome lattice
Beijing Computational Science Research Center（北京计算科学研究中心）；College of Physics and Electronic Engineering, Chongqing Normal University（重庆师范大学物理与电子工程学院）；Department of Physics, University of Houston（休斯顿大学物理系）；Texas Center for Superconductivity, University of Houston（休斯顿大学超导电性中心）
The phase diagram of the attractive Hubbard model with spatially inhomogeneous interactions is obtained using a single site dynamical mean field theory like approach. The model is characterized by three parameters: the interaction strength, the active fraction (fraction of sites with the attractive interaction), and electron filling. The calculations indicate that in a parameter regime with intermediate values of interaction strength (compared to the bare bandwidth of the electrons), and intermediate values of the active fraction, "non-BCS" superconductivity is obtained. The results of this wo…
We propose a fully microscopic theory of the anomalous normal state of the attractive Hubbard model in the low-density limit that accounts for propagator renormalization. Our analytical conclusions, which focus on the thermodynamic instabilities contained in the self-consistent equations associated with our formulation, have been verified by our comprehensive numerical study of the same equations. The resulting theory is found to contain no transitions at non-zero temperatures for all finite lattices, and we have confirmed, using our numerical studies, that this behaviour persists in the therm…
The influence of a Zeeman magnetic field on the superconducting characteristics of the attractive Hubbard model was investigated. The ground state and temperature phase diagrams were obtained for a fixed number of particles. Two critical magnetic fields were found for the first order phase transition from the superconducting to the normal state for $n\neq 1$. For some range of parameters a reentrant transition was found and gapless superconductivity was obtained. The significance of the Hartree term was also analyzed.
We investigate by means of Dynamical Mean-Field Theory the crossover from BCS superconductivity to Bose-Einstein (BE) condensation of preformed pairs in the attractive Hubbard model. We follow the evolution of the two energy scales underlying the superconducting phenomenon, the gap $Δ_0$ and the superfluid stiffness $D_S$, which controls the phase coherence. The BCS-BE crossover is clearly mirrored in a change in the hierarchy of these two scales, the smallest of the two controlling the critical temperature. In the whole intermediate-to-strong coupling region $T_c$ scales with $D_S$, while $T_…
We propose an extended Hubbard model on a 2D Kagome lattice with an additional ring-exchange term. The particles can be either bosons or spinless fermions . At a special filling fraction of 1/6 the model is analyzed in the lowest non-vanishing order of perturbation theory. Such ``undoped'' model is closely related to the Quantum Dimer Model. We show how to arrive at an exactly soluble point whose ground state manifold is the extensively degenerate ``d-isotopy space'', a necessary precondition for for a certain type of non-Abelian topological order. Near the ``special'' values, $d = 2 \cos π/(k…
We consider the extended Hubbard model with attractive on-site interaction U and nearest-neighbor repulsions V. We construct an effective Hamiltonian H_{eff} for hopping t<<V and arbitrary U<0. Retaining the most important terms, H_{eff} can be mapped onto two XXZ models, solved by the Bethe ansatz. The quantum phase diagram shows two Luttinger liquid phases and a region of phase separation between them. For density n<0.422 and U<-4, singlet superconducting correlations dominate at large distances. For some parameters, the results are in qualitative agreement with experiments in BaKBiO.
We have made a variational analysis on an evolution of superconductivity from weak to strong coupling regime. In contrast to a crossover without thermodynamic anomaly found in a dilute system, we show the existence of a quantum phase transition near half filling. The transition is driven by charge density waves instabilities. We have found that superconductivity and charge density waves coexist in the presence of a weak intersite repulsion. The ground state phase diagram is determined and the quantum phase transition is an attractive version of the Mott transition.
We study two-component fermions in optical lattices with spatially alternating on-site interactions using dynamical mean-field theory. Calculating the quasi-particle weight, double occupancy, and order parameters for each sublattice, we discuss the low-temperature properties of the system. When both interactions are repulsive, the magnetically ordered state is realized at half-filling. In the attractive case, the superfluid state is, in general, realized with a particle number imbalance. On the other hand, when repulsive and attractive interactions are comparable in the half-filled system, the…
This short paper summarizes a calculational method for obtaining the dynamical properties of many-body theories formulated in terms of (unrenormalized) bare propagators (and more generally, in terms of meromorphic functions, or convolutions over meromorphic functions) to a very high accuracy. We demonstrate the method by applying it to a T-matrix theory of the attractive Hubbard model in two dimensions. We expand the pair propagator using a partial fraction decomposition, and then solve for the residues and pole locations of such a decomposition using a computer algebra system to an arbitraril…
