We study the ground state of the one-dimensional extended Hubbard model at half-filling using the entanglement entropy calculated by Density Matrix Renormalization Group (DMRG) techniques. We apply a novel curve fitting and scaling method to accurately identify a $2^{nd}$ order critical point as well as a Berezinskii-Kosterlitz-Thouless (BKT) critical point. Using open boundary conditions and medium-sized lattices with very small truncation errors, we are able to achieve similar accuracy to previous authors. We also report observations of finite-size and boundary effects that can be remedied with careful pinning.
We consider dynamical spin-spin correlation functions in the one dimensional repulsive half-filled Hubbard model. We propose an exact expression for the two spinon formfactor of spin operators. We use this to derive the two spinon contribution to the dynamical structure factor.
We derive an effective spin Hamiltonian for the one-dimensional half-filled Alternating Hubbard model in the limit of strong on-site repulsion. We show that the effective Hamiltonian is a spin $S=1/2$ Heisenberg chain with asymmetric next-nearest-neighbor (nnn) exchange.
We derive an effective spin Hamiltonian for the one-dimensional half-filled tetramerized ionic-Hubbard model in the limit of strong on-site repulsion. We show that the effective Hamiltonian which describes the low-energy spin sector of the model is a spin S=1/2 Heisenberg Hamiltonian with alternating nearest-neighbour exchange.
We demonstrate that supervised machine learning (ML) with entanglement spectrum can give useful information for constructing phase diagram in the half-filled one-dimensional extended Hubbard model. Combining ML with infinite-size density-matrix renormalization group, we confirm that bond-order-wave phase remains stable in the thermodynamic limit.
Using the nonlocal coherent-potential approximation we study the effect of intersite spatial correlations on the transition from band insulator to metal as well as from metal to Mott insulator in the "alloy analogy" approach to the paramagnetic solution of the half-filled ionic Hubbard model. We find that intersite spatial correlations enhance the metallic phase.
We study interplay of electronic correlation, randomness and dimensionality effects in half-filled random Hubbard chains weakly coupled via an interchain one-particle hopping. Based on the two-loop renormalization-group approach, phase diagrams are given in terms of temperature vs. strengths of the intrachain electron-electron umklapp scattering, the random scattering and the interchain one-particle hopping.
The internal structure of stripes in the two dimensional Hubbard model is studied by going beyond the Hartree-Fock approximation. Partially filled stripes, consistent with experimental observations, are stabilized by quantum fluctuations, included through the Configuration Interaction method. Hopping of short regions of the stripes in the transverse direction is comparable to the bare hopping element. The integrated value of $n_{\bf \vec{k}}$ compares well with experimental results.
We study antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model at low temperature. Collective spin fluctuations are governed by a non-linear sigma model that we derive from the Hubbard model for any value of the Coulomb repulsion. As the Coulomb repulsion increases, the ground state progressively evolves from a Slater to a Mott-Heisenberg antiferromagnet. At finite temperature, we find a metal-insulator transition between a pseudogap phase at weak coupling and a Mott-Hubbard insulator at strong coupling.
Two very different methods -- exact diagonalization on finite chains and a variational method -- are used to study the possibility of a metal-insulator transition in the symmetric half-filled periodic Anderson-Hubbard model. With this aim we calculate the density of doubly occupied $d$ sites as a function of various parameters. In the absence of on-site Coulomb interaction ($U_f$) between $f$ electrons, the two methods yield similar results. The double occupancy of $d$ levels remains always finite just as in the one-dimensional Hubbard model. Exact diagonalization on finite chains gives the sa…
We investigate the antiferromagnetically ordered state in the half-filled Hubbard model on the Socolar dodecagonal tiling. When the interaction is introduced, the staggered magnetizations suddenly appear, which results from the existence of the macroscopically degenerate states in the tightbinding model. The increase of the interaction strength monotonically increases the magnetizations although its magnitude depends on the local environments. Magnetization profile is discussed in the perpendicular space. The similarity and difference are also addressed in magnetic properties in the Hubbard mo…
We present a highly parallelisable scheme for treating functional Renormalisation Group equations which incorporates a quasi-particle-based feedback on the flow and provides direct access to real-frequency self-energy data. This allows to map out the boundaries of Fermi-liquid regimes and to study the effect of quasi-particle degradation near Fermi liquid instabilities. As a first application, selected results for the two-dimensional half-filled perfectly nested Hubbard model are shown.
We investigate the half-filled two-orbital Hubbard model with the crystalline electric field using dynamical mean-field theory combined with the continuous-time quantum Monte Carlo simulations. We systematically study how the interplay of the intra- and interorbital Coulomb interations together with the Hund coupling realizes the diagonal and off-diagonal ordered states. It is found that the antiferroorbital ordered state is realized in the Hubbard model, in addition to the antiferromagnetically ordered and excitonic states. The competition between the antiferroorbital ordered and excitonic st…
We derive an effective spin Hamiltonian for the one-dimensional half-filled asymmetric ionic Hubbard model with alternating on-site interaction in the limit of strong repulsion. It is shown that the effective Hamiltonian is that of a spin $S=1/2$ anisotropic $XXZ$ Heisenberg chain with alternating next-nearest-neighbor and three-spin couplings in the presence of a uniform and a staggered magnetic field.
The half-filled extended Hubbard model, in one and two dimensions, is studied by means of the 2-pole approximation within the Composite Operator Method with the aim at improving the possibilities to describe some of the experimental features observed for quasi-1D organic superconductors and Cu-O planes of cuprates. The phase diagrams ($T$-$V$ and $V$-$U$) are analyzed with respect to the paramagnetic metal - paramagnetic insulator - charge ordered phase transitions. The relevant features of the diagrams (rank of the phase transitions, critical points, reentrant behavior) are discussed in detai…
We obtain the phase-diagram of the half-filled honeycomb Hubbard model with density matrix embedding theory, to address recent controversy at intermediate couplings. We use clusters from 2-12 sites and lattices at the thermodynamic limit. We identify a paramagnetic insulating state, with possible hexagonal cluster order, competitive with the antiferromagnetic phase at intermediate coupling. However, its stability is strongly cluster and lattice size dependent, explaining controver- sies in earlier work. Our results support the paramagnetic insulator as being a metastable, rather than a true, i…
In this paper we investigate effects of a lattice dimension on strongly correlated electronic systems at $T=0 K$. The model for numerical calculations is formalized in terms of the integral equations which were obtained previously for the half -- filled paramagnetic Hubbard model. The assumption that all relevant functions of the system have a magnitude dependence of momentus vectors makes ultimately possible treating a lattice dimension $D$ as an external parameter. We here submit for consideration the number of doubly occupied lattice sites, the electronic density of states, and the momentum…
We consider density-density correlations in the one-dimensional Hubbard model at half filling. On intuitive grounds one might expect them to exhibit an exponential decay. However, as has been noted recently, this is not obvious from the Bethe Ansatz/conformal field theory (BA/CFT) approach. We show that by supplementing the BA/CFT analysis with simple symmetry arguments one can easily prove that correlations of the lattice density operators decay exponentially.
The 2D half-filled Hubbard model is studied by a nonperturbative analytic theory of correlator projection. The original dynamical mean-field approximation (DMFA) is reproduced at the first-order projection and then improved by systematic inclusion of spatial correlations at higher orders. A geometrical frustration induces a first-order Mott transition surface with a finite-temperature critical end curve. Growth of antiferromagnetic correlations gives single-particle spectra strongly modified from DMFA with shadow bands and flat dispersions observed in high-T_c cuprates.
The magnetic properties and Mott transition of the half-filled Hubbard model on the 1/5 depleted square lattice with frustration is studied at zero temperature by the variational cluster approximation. The $(π,π)$ Néel ordering (AF) is stable in a wide region of the phase diagram and almost completely veils the non-magnetic Mott transition for the unfrustrated case. However, AF is severely suppressed by the frustration and even with moderate frustrations the non-magnetic Mott transition takes place in the range where the intra-dimer hoppings are larger than the intra-plaquette hoppings.
Using a self-consistent Hartree-Fock approximation we investigate the relative stability of various stripe phases in the extended $t$-$t'$-$U$ Hubbard model. One finds that a negative ratio of next- to nearest-neighbor hopping $t'/t<0$ expells holes from antiferromagnetic domains and reinforces the stripe order. Therefore the half-filled stripes not only accommodate holes but also redistribute them so that the kinetic energy is gained, and these stripes take over in the regime of $t'/t\simeq -0.3$ appropriate for YBa$_2$Cu$_3$O$_{6+δ}$.
The electronic properties of the quarter-filled extended Peierls-Holstein-Hubbard model that includes lattice distortions and molecular deformations are investigated theoretically using the bosonization approach. We predict the existence of a wide variety of charge-elastic phases depending of the values of the Peierls and Holstein couplings. We include the effect of the Peierls deformation in the nearest-neighbor repulsion V, that may be present in real materials where Coulomb interactions depend strongly on the distance, and we show that the phase diagram changes substantially for large V whe…
We analyze the Thermodynamic Bethe Ansatz equations of the one-dimensional half-filled Hubbard model in the "spin-disordered regime", which is characterized by the temperature being much larger than the magnetic energy scale but small compared to the Mott-Hubbard gap. In this regime the thermodynamics of the Hubbard model can be thought of in terms of gapped charged excitations with an effective dispersion and spin degrees of freedom that only contribute entropically. In particular, the internal energy and the effective dispersion become essentially independent of temperature. An interpretatio…
We have studied the influence of nearest-neighbor (NN) repulsion on the low frequency phase diagram of a quarter-filled Hubbard-Holstein chain. The NN repulsion term induces the apparition of two new long range ordered phases (one $4k_F$ CDW for positive $U_{eff} = U-2g^2/ω$ and one $2k_F$ CDW for negative $U_{eff}$) that did not exist in the V=0 phase diagram. These results are put into perspective with the newly observed charge ordered phases in organic conductors and an interpretation of their origin in terms of electron-molecular vibration coupling is suggested.
The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any nonzero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within the Bethe Ansatz. These results show that the Composite Operator Method is an appropriate framework for the half-filled Hubbard chain and can be applied to evaluate properties, like the correlation functions…
The two-dimensional Peierls-Hubbard model is studied at half-filling within both Hartree-Fork and Kotliar-Ruckenstein slave-boson theory. The interplay between two types of long-range order, bond-order wave (BOW) and antiferromagnetism (AFM), is analysed for two representative dimerization patterns, corresponding both to the same wavevector $(π,π)$. For each pattern, the Peierls dimerization (and associated BOW) is weakened and finally suppressed with increasing Hubbard on-site interaction, and correspondingly AFM is gradually enhanced. In particular, a coexistence regime with both BOW and AFM…
By the example of the Hubbard model we analytically and numerically examine the formating and coexisting of localized electron--electron pairs (doublons) and localized electron--hole pairs (Frenkel--type excitons) . Here we demonstrate that at a variation of the on-site Coulomb repulsion U there occurs a quantum transition from the doublon to the exciton regime that is conditioned by the low-energy effective hybridization of the valence and conductivity subbands. We calculate momentum distribution functions and electronic spectrum functions for different U, which reveal topologically nontrivia…
In order to clarify the physics of the crossover from a spin-density-wave (SDW) Mott insulator to a charge-density-wave (CDW) Peierls insulator in one-dimensional (1D) systems, we investigate the Hubbard-Holstein Hamiltonian at half filling within a density matrix renormalisation group (DMRG) approach. Determining the spin and charge correlation exponents, the momentum distribution function, and various excitation gaps, we confirm that an intervening metallic phase expands the SDW-CDW transition in the weak-coupling regime.
We use a density matrix renormalization group method to study quantitatively the phase diagram of a one-dimensional extended Hubbard model at half-filling by investigating the correlation functions and structure factors. We confirm the existence of a novel narrow region with long-rang bond-order-wave order which is highly controversial recently between the charge-density-wave phase and Mott insulator phase. We determined accurately the position of the tricritical point $U_t\simeq 7.2t$, $V_t\simeq 3.746t$ which is quite different from previous studies.
We study the low-energy asymptotics of the half-filled Hubbard model with a circular Fermi surface in $d=1+ε$ continuous dimensions, based on the one-loop renormalization-group (RG) method. Peculiarity of the $d=1+ε$ dimensions is incorporated through the mathematica structure of the elementary particle-partcile (PP) and particle-hole (PH) loops: infrared logarithmic singularity of the PH loop is smeared for $ε>0$. The RG flows indicate that a quantum phase transition (QPT) from a metallic phase to the Mott insulator phase occurs at a finite on-site Coulomb repulsion $U$ for $ε>0$. We also dis…
Magnetic properties in a charge ordered state are examined for the extended Hubbard model at half-filling. Magnetic excitations, magnetic susceptibilities and a nuclear spin relaxation rate are calculated with taking account of fluctuations around the mean-field solution. The relevance of the present results to the observation in the 1:1 organic conductors, (TTM-TTP)I$_3$, is discussed.
We study a two-dimensional Hubbard-Holstein model with phonons treated in the adiabatic limit. A Hartree-Fock decomposition is employed for the Hubbard term. A range of electronic densities are discussed with special emphasis on the quarter-filling ($n=0.5$). We argue that the quarter-filled system is relevant for the electronic properties observed at the interface between LaAlO$_3$ and SrTiO$_3$, where half-electron per unit cell is transferred to the TiO$_2$ layer as a consequence of the polar discontinuity at the interface. In addition to presenting the overall phase diagrams, we identify a…
A detailed study of electronic phase transitions in the ionic Hubbard model at half filling is presented. Within the dynamical mean field approximation a series of transitions from the band insulator via a metallic state to a Mott-Hubbard insulating phase is found at intermediate values of the one-body potential $Δ$ with increasing the Coulomb interaction $U$. We obtain a critical region in which the metallic phase disappears and a {\it novel} coexistence phase between the band and the Mott insulating state sets in. Our results are consistent with those obtained at low dimensions, thus they pr…
We investigate the ground-state phase diagram of the half-filled one-dimensional Hubbard model with next-nearest-neighbor hopping using the Density-Matrix Renormalization Group technique as well as an unrestricted Hartree-Fock approximation. We find commensurate and incommensurate disordered magnetic insulating phases and a spin-gapped metallic phase in addition to the one-dimensional Heisenberg phase. At large on-site Coulomb repulsion $U$, we make contact with the phase diagram of the frustrated Heisenberg chain, which has spin-gapped phases for sufficiently large frustration. For weak $U$, …
The electronic system of the 1D Hubbard model is not stable due to Peierls instability; the correlations are strong even for the weak Coulomb interaction. The resulting strongly correlated state without Landau quisi--particle excitations is known as the Luttinger liquid. Critical exponents of a power--law dependence of correlation functions at low energies differ substantially for the Luttinger and Fermi liquids. In this paper we evaluate two critical exponents that define non--trivial behavior of the density of electronic states at low frequences and the momentum distribution of the occupatio…
The effective spin Hamiltonian is constructed in the framework of the almost half-filled Hubbard model on the Cayley tree by means of functional integral technique with the use of static approximation. The system in the ground state appears to be consisting of the ferromagnetic metallic domains and the antiferromagnetic insulating one sprovided that the concentration of excess electrons (or holes) does not exceed some critical value. The connection between the Hubbard model and the {\it s-f} model is stated. Note added: This posting is intended to show that the phase separation in strongly cor…
We study the time evolution of a half-filled Hubbard layer coupled to a magnon bath after a quench of the Hubbard interaction. Qualitatively different regimes, regarding the asymptotic long-time dynamics, are identified and characterized within the mean-field approximation. In the absence of the bath, the dynamics of the closed system is similar to that of a quenched BCS condensate. Though the presence of the bath introduces an additional relaxation mechanism, our numerical results and analytical arguments show that equilibration with the bath is not necessarily attained within the approximati…
We use Brueckner-Goldstone perturbation theory to calculate the ground-state energy of the half-filled Hubbard model in infinite dimensions up to fourth order in the Hubbard interaction. We obtain the momentum distribution as a functional derivative of the ground-state energy with respect to the bare dispersion relation. The resulting expressions agree with those from Rayleigh-Schroedinger perturbation theory. Our results for the momentum distribution and the quasi-particle weight agree very well with those obtained earlier from Feynman-Dyson perturbation theory for the single-particle self-en…
An extended Hubbard model (including nearest-neighbor repulsion and antiferromagnetic spin exchange) is investigated on the frustrated checkerboard lattice, a two-dimensional analog of the pyrochlore lattice. Combining Gutzwiller renormalized mean-field (MF) calculations, exact diagonalization (ED) techniques, and a weak-coupling renormalization group (RG) analysis we provide strong evidence for a crystalline valence bond plaquette phase at quarter-filling. The ground state is twofold degenerate and breaks translation symmetry. The bond energies show a staggering while the charge distribution …
The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion, and hopping t. A critical line V_c(U) approximately equal to U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V > 2t changes the phase transition from continuous to first order at a tricritical point U_t = 3.7t, V_t=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V_c(U) for U_t < U < 7-8…
Motivated by Mo$_3$S$_7$(dmit)$_3$, we investigate the Hubbard model on the triangular necklace lattice at two-thirds filling. We show, using second order perturbation theory, that in the molecular limit, the ground state and the low energy excitations of this model are identical to those of the spin-one Heisenberg chain. The latter model is known to be in the symmetry protected topological Haldane phase. Away from this limit we show, on the basis of symmetry arguments and density matrix renormalization group (DMRG) calculations, that the low-energy physics of the Hubbard model on the triangul…
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 their Comment (see cond-mat/0301237), Sandvik, Sengupta, and Campbell present some numerical evidences to support the existence of an extended bond-order-wave (BOW) phase at couplings (U,V) weaker than a tricritical point (U_t,V_t) in the ground state phase diagram of the one-dimensional half-filled U-V Hubbard model. They claim that their results do not agree with the phase diagram proposed in my Letter (cond-mat/0204244), which shows a BOW phase for couplings stronger than the critical point only. However, I argue here that their results are not conclusive and do not refute the phase diag…
We study the interplay between Néel-antiferromagnetism and the paramagnetic metal-insulator-transition (PMIT) on a Bethe lattice with nearest and next-nearest eighbor hopping $t_1$ and $t_2$. We concentrate in this paper on the situation at half-filling. For $t_2/t_1\to 1$ the PMIT outgrows the antiferromagnetic phase and shows a scenario similar to V$_2$O$_3$. In this parameter regime we also observe a novel magnetic phase.
By means of the dynamical vertex approximation (D$Γ$A) we include spatial correlations on all length scales beyond the dynamical mean field theory (DMFT) for the half-filled Hubbard model in three dimensions. The most relevant changes due to non-local fluctuations are: (i) a deviation from the mean-field critical behavior with the same critical exponents as for the three dimensional Heisenberg (anti)-ferromagnet and (ii) a sizable reduction of the Néel temperature ($T_N$) by $\sim 30%$ for the onset of antiferromagnetic order. Finally, we give a quantitative estimate of the deviation of the sp…
Starting from the Hubbard model in the weak-coupling limit, we derive a spin-fermion model where the collective spin excitations are described by a non-linear sigma model. This result is used to compute the fermion spectral function $A({\bf k},ω)$ in the low-temperature regime where the antiferromagnetic (AF) coherence length is exponentially large (``renormalized classical'' regime). At the Fermi level, $A({\bf k}_F,ω)$ exhibits two peaks around $\pmΔ_0$ (with $Δ_0$ the mean-field gap), which are precursors of the zero-temperature AF bands, separated by a pseudogap.
Using quantum Monte Carlo simulations, results of a strong-coupling expansion, and Luttinger liquid theory, we determine quantitatively the ground state phase diagram of the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsions U and V. We show that spin frustration stabilizes a bond-ordered (dimerized) state for U appr. V/2 up to U/t appr. 9, where t is the nearest-neighbor hopping. The transition from the dimerized state to the staggered charge-density-wave state for large V/U is continuous for U up to appr. 5.5 and first-order for higher U.
In Phys. Rev. Lett. 89, 236401 (2002), Jeckelmann argued that the recently discovered bond-order-wave (BOW) phase of the 1D extended Hubbard model does not have a finite extent in the (U,V) plane, but exists only on a segment of a first-order SDW-CDW phase boundary. We here present quantum Monte Carlo result of higher precision and for larger system sizes than previously and reconfirm that the BOW phase does exist a finite distance away from the phase boundary, which hence is a BOW-CDW transition curve.
We investigate the ground-state phase diagram of the one-dimensional "ionic" Hubbard model with an alternating periodic potential at half-filling by numerical diagonalization of finite systems with the Lanczos and density matrix renormalization group (DMRG) methods. We identify an insulator-insulator phase transition from a band to a correlated insulator with simultaneous charge and bond-charge order. The transition point is characterized by the vanishing of the optical excitation gap while simultaneously the charge and spin gaps remain finite and equal. Indications for a possible second trans…
The metal-insulator transition of the quarter-filled Hubbard model on triangular lattice is studied at the mean field level. We find a quasi-one dimensional metallic state with a collinear magnetic order competes closely with an insulating state with a non-coplanar magnetic order for both signs of the hopping integral $t$. In the strong correlation regime($U/|t|\gg1$), it is found that the metal-insulator transition of the system occurs in a two-step manner. The quasi-one dimensional metallic state with collinear magnetic order is found to be stable in an intermediate temperature region betwee…
We analyze the ground-state properties of strongly-correlated electrons coupled with phonons by means of a generalized Gutzwiller wavefunction which includes phononic degrees of freedom. We study in detail the paramagnetic half-filled Hubbard-Holstein model, where the electron-electron interaction can lead to a Mott transition, and the electron-phonon coupling to a bipolaronic transition. We critically discuss the quality of the proposed wavefunction in describing the various transitions and crossovers that occur as a function of the parameters. Previous variational attempts are recovered as p…
We calculate the zero-temperature self-energy to fourth-order perturbation theory in the Hubbard interaction $U$ for the half-filled Hubbard model in infinite dimensions. For the Bethe lattice with bare bandwidth $W$, we compare our perturbative results for the self-energy, the single-particle density of states, and the momentum distribution to those from approximate analytical and numerical studies of the model. Results for the density of states from perturbation theory at $U/W=0.4$ agree very well with those from the Dynamical Mean-Field Theory treated with the Fixed-Energy Exact Diagonaliza…
We combine well-controlled analytical and numerical methods to determine the optical conductivity of the one-dimensional Mott-Hubbard insulator at zero temperature. A dynamical density-matrix renormalization group method provides the entire absorption spectrum for all but very small coupling strengths. In this limit we calculate the conductivity analytically using exact field-theoretical methods. Above the Lieb-Wu gap the conductivity exhibits a characteristic square-root increase. For small to moderate interactions, a sharp maximum occurs just above the gap. For larger interactions, another w…
We have studied a Hubbard ring with alternating site potentials for half filling in presence of a magnetic flux. Using a mean field approach we have calculated the conductivity of such a ring at low and high temperatures. The interplay of correlation, the polarizing field and the chemical modulation in the site potentials tune the conductivity in an interesting fashion. In presence of the modulation in the site energy an appreciable variation in the conductance is observed with the change in flux. Finite size effects are also identified and they are found to be quickly disappearing with increa…
The magnon propagator is evaluated in the AF (π,π,π) and the F-AF (0,π,π) states at the RPA level, and the spin-fluctuation corrections are compared. Transverse spin fluctuations are sharply enhanced by the frustration- inducing NNN hopping t', reducing the zero-temperature AF order in two dimensions, and the Neel temperature in three dimensions. The phase boundary between the insulating AF and F-AF states is obtained in the full range of interaction strength, indicating that the AF state is interestingly stabilized with decreasing U.
We study magnetic, transport and thermodynamic properties of the half-filled two-dimensional ($2D$) Hubbard model with layered distributed repulsive interactions using unbiased finite temperature quantum Monte Carlo simulations. Antiferromagnetic long-ranged correlations at $T=0$ are confirmed by means of the magnetic structure factor and the onset of short-ranged ones is at a minimum temperature which can be obtained by peaks in susceptibility and specific heat following an RPA prediction. We also show that transport is affected in the large interaction limit and is enhanced in the non-repuls…
We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling using a novel functional renormalization group (FRG) approach. The FRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi points. Our results confirm the existence of a finite region of bond charge density wave (BCDW), also known as a ``bond order wave'' (BOW), near $U = 2V$ and clarify why earlier g-ology calculations have not found this phase. We argue that this is an example in which formally irrelevant corrections change t…
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…
We describe a low-temperature approach to the two-dimensional half-filled Hubbard model which allows us to study both antiferromagnetism and single-particle properties. This approach ignores amplitude fluctuations of the antiferromagnetic (AF) order parameter and is valid below a crossover temperature $T_X$ which marks the onset of AF short-range order. Directional fluctuations (spin waves) are described by a non-linear sigma model (NL$σ$M) that we derive from the Hubbard model. At zero temperature and weak coupling, our results are typical of a Slater antiferromagnet. The AF gap is exponentia…
