2D Hubbard Model Research Articles

Ground-state properties of 1D Hubbard model in optical superlattice

We study the ground-state properties of a cold Fermi gas trapped in a one-dimensional optical superlattice with periodically modulated lattice potentials. By applying the density matrix renormalization group method to the Hubbard model with harmonic confinement, we compute the density profile and the spin correlation function for several different choices of superlattice potential. The ground state is characterized by the coexistence phase with the metallic and several types of Mott-insulating domains. It is shown that the spin correlation can be enhanced between the two spatially separated Mott-insulating domains.

Anomalous temperature dependence of the single-particle spectrum in the organic conductor TTF-TCNQ

The angle-resolved photoemission spectrum of the organic conductor TTF-TCNQ exhibits an unusual transfer of spectral weight over a wide energy range for temperatures $60\phantom{\rule{0.3em}{0ex}}\mathrm{K}<T<260\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. In order to investigate the origin of this finding, here we report numerical results on the single-particle spectral weight $A(k,\ensuremath{\omega})$ for the one-dimensional (1D) Hubbard model and, in addition, for the 1D extended Hubbard and the 1D Hubbard-Holstein models. Comparisons with the photoemission data suggest that the 1D Hubbard model is not sufficient for explaining the unusual $T$ dependence, and the long-range part of the Coulomb repulsion also needs to be included.

Fermi Liquid Behavior in the 2D Hubbard Model at Low Temperatures

We prove that the weak coupling 2D Hubbard model away from half filling is a Landau Fermi liquid up to exponentially small temperatures. In particular we show that the wave function renormalization is an order 1 constant and essentially temperature independent in the considered range of temperatures and that the interacting Fermi surface is a regular convex curve. This result is obtained by deriving a convergent expansion (which is not a power series) for the two point Schwinger function by Renormalization Group methods and proving at each order suitable power counting improvements due to the convexity of the interacting Fermi surface. Convergence follows from determinant bounds for the fermionic expectations.

Renormalization group calculation of the uniform susceptibilities in low-dimensional systems

We analyze the one-dimensional (1D) and the two-dimensional (2D) repulsive Hubbard models (HM) for densities slightly away from half-filling through the behavior of two central quantities of a system: the uniform charge and spin susceptibilities. We point out that a consistent renormalization group treatment of them can only be achieved within a two-loop approach or beyond. In the 1D HM, we show that this scheme reproduces correctly the metallic behavior given by the well-known Luttinger liquid fixed-point result. Then, we use the same approach to deal with the more complicated 2D HM. In this case, we are able to show that both uniform susceptibilities become suppressed for moderate interaction parameters as one take the system towards the Fermi surface. Therefore, this result adds further support to the interpretation that those systems are in fact insulating spin liquids. Later, we perform the same calculations in 2D using the conventional random phase approximation, and establish clearly a comparison between the two schemes.

Superconducting condensation energy computed for the 2D Hubbard model with Bi2212-type band

The 2D Hubbard model is the simplest model that possibly explains the occurrence of high-Tc superconductivity (SC) in cuprates. To demonstrate this possibility with a condition of moderate on-site Coulomb energy U, we have computed the SC condensation energy Econd by means of the variational Monte Carlo method employing a slightly modified Gutzwiller trial wave function which also takes account of the Bi2212-type band, i.e., t′∼−0.34 and t″∼0.23 (t, t′ and t″ are defined in the main text; energy unit is t). The competing SDW Econd strongly depended on the employed lattice size L×L but approached the bulk-limit value when L⩾16. With proper assumption on the value of t″, the t′ region where the SDW Econd are larger than the SC Econd shrank to −0.16⩽t′⩽−0.08. In −0.40<t′<−0.16 the SC Econd was found predominant. Concerning the lattice-size dependence the SC Econd in the neighborhood of the Bi2212-type set was found to tend to increase with increasing L when L⩾16, taking about 1/3 or 1 times the experimental SC Econd of YBCO. This was computed using periodic boundary conditions (bc’s) for the two directions. The average of two results for periodic and antiperiodic bc’s imposed to both x- and y-directions for t′=−0.31 and t″=0.21 proved to make the L-dependence so mild that the extrapolation to the finite bulk limit looks plausible. Together with the previous positive result with t′∼−0.05 and t″=0, this result clearly supports the applicability of the 2D Hubbard model to the SC in the whole group of cuprates. Incidentally, more elaborate Gutzwiller–Jastrow-type trial functions were also examined but found to bring in only minor differences.

Separation of spin and charge in cold Fermi gases

One of the key features of one-dimensional systems is the phenomenon of spin–charge separation. We show this separation of spin and charge in real time in the 1D Hubbard model by the application of the adaptive time-dependent density-matrix renormalization group method. It is found for single particle excitations and density wave packets far beyond the low-energy Luttinger liquid theory. An experimental set-up is proposed on how to observe the spin–charge separation with ultracold Fermi gases in a harmonic trap using the presence of the Mott-insulator region. Quantitative estimates for experimental parameters are given.

Single-site entanglement of fermions at a quantum phase transition

We show that the single-site entanglement of a generic spin-1/2 fermionic lattice system can be used as a reliable marker of a finite-order quantum phase transition, given certain provisos. We discuss the information contained in the single-site entanglement measure, and provide illustrations from the Mott--Hubbard metal-insulator transitions of the one-dimensional (1D) Hubbard model, and the (1D) Hubbard model with long-range hopping.

Correlation-function asymptotic expansions: Universality of prefactors of the one-dimensional Hubbard model

We show that the prefactors of all terms of the one-dimensional (1D) Hubbard model correlation-function asymptotic expansions have a universal form, as the corresponding critical exponents. In addition to calculating such prefactors, our study clarifies the relation of the low-energy Tomonaga-Luttinger-liquid behavior to the scattering mechanisms which control the spectral properties of the model at all energy scales. Our results are of general nature for many integrable interacting models and provide a broader understanding of the unusual properties of quasi-1D nanostructures, organic conductors, and optical lattices of fermionic atoms.

Insulating spin liquid in the lightly doped two-dimensional Hubbard model

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 insulating state.

Rigorous Proof of Luttinger Liquid Behavior in the 1d Hubbard Model

We give the first rigorous (non perturbative) proof of Luttinger liquid behavior in the one dimensional Hubbard model, for small repulsive interaction and values of the density different from half filling. The analysis is based on the combination of multiscale analysis with Ward identities based on a hidden and approximate local chiral gauge invariance. No use is done of exact solutions or special integrability properties of the Hubbard model, and the results can be in fact easily generalized to include non local interactions, magnetic fields or interaction with external potentials

Spin-Charge Separation in Cold Fermi Gases: A Real Time Analysis

Using the adaptive time-dependent density-matrix renormalization group method for the 1D Hubbard model, the splitting of local perturbations into separate wave packets carrying charge and spin is observed in real time. We show the robustness of this separation beyond the low-energy Luttinger liquid theory by studying the time evolution of single particle excitations and density wave packets. A striking signature of spin-charge separation is found in 1D cold Fermi gases in a harmonic trap at the boundary between liquid and Mott-insulating phases. We give quantitative estimates for an experimental observation of spin-charge separation in an array of atomic wires.

Efficient calculation of the antiferromagnetic phase diagram of the three-dimensional Hubbard model

The Dynamical Cluster Approximation with Betts clusters is used to calculate the antiferromagnetic phase diagram of the 3D Hubbard model at half filling. Betts clusters are a set of periodic clusters which best reflect the properties of the lattice in the thermodynamic limit and provide an optimal finite-size scaling as a function of cluster size. Using a systematic finite-size scaling as a function of cluster space-time dimensions, we calculate the antiferromagnetic phase diagram. Our results are qualitatively consistent with the results of Staudt et al. [Eur. Phys. J. B 17 411 (2000)], but require the use of much smaller clusters: 48 compared to 1000.

Temperature dependence of spinon and holon excitations in one-dimensional Mott insulators

Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) measurements on one-dimensional Mott insulators, SrCuO${}_{2}$ and Na${}_{0.96}$V${}_{2}$O${}_{5}$, we examine the single-particle spectral weight of the one-dimensional (1D) Hubbard model at half-filling. We are particularly interested in the temperature dependence of the spinon and holon excitations. For this reason, we have performed the dynamical density matrix renormalization group and determinantal quantum Monte Carlo (QMC) calculations for the single-particle spectral weight of the 1D Hubbard model. In the QMC data, the spinon and holon branches become observable at temperatures where the short-range antiferromagnetic correlations develop. At these temperatures, the spinon branch grows rapidly. In the light of the numerical results, we discuss the spinon and holon branches observed by the ARPES experiments on SrCuO${}_{2}$. These numerical results are also in agreement with the temperature dependence of the ARPES results on Na${}_{0.96}$V${}_{2}$O${}_{5}$.

Studies on entanglement entropy for Hubbard model with hole-doping and external magnetic field

By using the density matrix renormalization group (DMRG) method for the one-dimensional (1D) Hubbard model, we have studied the von Neumann entropy of a quantum system, which describes the entanglement of the system block and the rest of the chain. It is found that there is a close relation between the entanglement entropy and properties of the system. The hole-doping can alter the charge–charge and spin–spin interactions, resulting in charge polarization along the chain. By comparing the results before and after the doping, we find that doping favors increase of the von Neumann entropy and thus also favors the exchange of information along the chain. Furthermore, we calculated the spin and entropy distribution in external magnetic filed. It is confirmed that both the charge–charge and the spin–spin interactions affect the exchange of information along the chain, making the entanglement entropy redistribute.

Existence of Solutions to the Bethe Ansatz Equations for the 1D Hubbard Model: Finite Lattice and Thermodynamic Limit

In this work, we present a proof of the existence of real and ordered solutions to the generalized Bethe Ansatz equations for the one dimensional Hubbard model on a finite lattice, with periodic boundary conditions. The existence of a continuous set of solutions extending from any positive U to the limit of large interaction is also shown. This continuity property, when combined with the proof that the wavefunction obtained with the generalized Bethe Ansatz is normalizable, is relevant to the question of whether or not the solution gives us the ground state of the finite system, as suggested by Lieb and Wu. Lastly, for the absolute ground state at half-filling, we show that the solution converges to a distribution in the thermodynamic limit. This limit distribution satisfies the integral equations that led to the well known solution of the 1D Hubbard model.

How effective are non-local fluctuations in the 2D Hubbard model at [formula omitted

We present the first DCA results for the 2D Hubbard model obtained with a suitably extended version of Wilson's NRG. We discuss the rôle of non-local fluctuations on the spectral properties at T → 0 for half-filling. In particular, we find that the system is a paramagnetic insulator for all U > 0 .

Physical properties of electrically conducting and stable molecular neutral radical solid [Co(2,3-Nc)(CN)2]CH3CN (2,3-Nc = 2,3-naphthalocyanine)

Solid state properties of dicyano(2,3-naphthalocyaninato)cobalt(III) neutral radical crystal, [ Co (2,3- Nc )( CN )2] CH 3 CN , were characterized by measurements of the resistivity under high pressure and under uniaxial strain, thermoelectric power, magnetic susceptibility, ESR and polarized reflectance spectra. The title compound exhibited thermally activated-type electrical conductivity along the c-axis. The room temperature (RT) resistivity ρRT along the c-axis and activation energy Ea rapidly decreased with increasing pressure. The temperature-dependent thermoelectric power S was that of a typical one-dimensional (1D) semiconductor. However the high absolute value of S suggested that this electronic system should be strongly correlated. Although the electrical resistivity exhibited monotonous temperature-dependence, the magnetic susceptibility clearly indicated a Peierls-type transition and marked fluctuation from RT. Both Peierls-type transitions and fluctuations are characteristic phenomena to 1D conductors. Furthermore ESR spectra manifested that the Peierls-type transition occurred at 100 K. The inconsistency between the electrical behavior (without a phase-transition) and magnetic behavior (with a phase-transition) indicates separation of the degrees of freedom in spin and charge (spin-charge separation) of this material. Spin-charge separation is a theoretically predicted phenomenon peculiar to the 1D conductors with strong correlation. The reflectance spectra were quantitatively explained by a 1D Hubbard model, and manifested the existence of a structural fluctuation of this material from RT. Based on these observed physical properties it is concluded that [ Co (2,3- Nc )( CN )2] CH 3 CN is a strongly correlated 1D semiconductor with a Mott(Hubbard) type energy gap and characterised with a fluctuation and spin-charge separation.

Quantum Monte Carlo study of the pairing symmetry competition in the Hubbard model

To shed light into the pairing mechanism of possible spin triplet superconductors ${(\text{TMTSF})}_{2}X$ and ${\text{Sr}}_{2}{\text{RuO}}_{4}$, we study the competition among various spin singlet and triplet pairing channels in the Hubbard model by calculating the pairing interaction vertex using the ground state quantum Monte Carlo technique. We model ${(\text{TMTSF})}_{2}X$ by a quarter-filled quasi-one-dimensional (quasi-1D) Hubbard model, and the $\ensuremath{\gamma}$ band of ${\text{Sr}}_{2}{\text{RuO}}_{4}$ by a two-dimensional (2D) Hubbard model with a band filling of $\ensuremath{\sim}4∕3$. For the quasi-1D system, we find that triplet $f$-wave pairing not only dominates over the triplet $p$ wave in agreement with the spin fluctuation theory, but also looks unexpectedly competitive against $d$ waves. For the 2D system, although the results suggest the presence of an attractive interaction in the triplet pairing channels, the $d$-wave pairing interaction is found to be larger than those of the triplet channels.

RVB and gossamer superconductivity

Gutzwiller variational method is applied to an effective 2D Hubbard model to examine the recently proposed gossamer superconductivity [LANL cond-mat/0209269 (2002)]. The ground state at half filled is a gossamer superconductor for smaller intrasite Coulomb repulsion U and a Mott insulator for larger U. The transition is of first type. Away from half filled, the gossamer superconductor is adiabatically evolved into the RVB superconducting state.

Nonperturbative approach to full Mott behavior

Though most fermionic Mott insulators order at low temperatures, ordering is ancillary to their insulating behaviour. Our emphasis here is on disentangling ordering from the intrinsic strongly correlated physics of a doped half-filled band. To this end, we focus on the 2D Hubbard model. Because the charge gap arises from on-site correlations, we implement a non-perturbative approach which incorporates local physics. Crucial to this method is a self-consistent two-site dynamical cluster expansion which builds in the nearest-neighbour energy scale, $J$. At half-filling, we find that the spectral function possesses a gap of order $U$ and is devoid of any coherent quasi-particle peaks. In the doped case, we find that the Fermi surface exceeds the Luttinger volume. Additionally in the underdoped regime, we find that a pseudogap opens in the single particle density of states.The pseudogap closes above optimal doping and hence our proposal is not inconsistent with that of Loram. In analogy with the Mott gap and antiferromagnetism, we propose that ordering may also accompany the formation of a pseudogap. We suggest a current pattern within a 1-band model that preserves translational but breaks time-reversal symmetry along the canonical x and y axes but not along $x=\pm y$ that is consistent with the experimental observations. Finally, we show that the Hall coefficient in a doped Mott insulator must change sign at a doping level $x<1/3$. The sign change is tied to a termination of strong correlation physics in the doped Mott state.