Dimerized Hubbard Model Research Articles

Level statistics of the one-dimensional dimerized Hubbard model

The statistical properties of level spacings provide valuable insights into the dynamical properties of a many-body quantum systems. We investigate the level statistics of the Fermi–Hubbard model with dimerized hopping amplitude and find that after taking into account translation, reflection, spin and η pairing symmetries to isolate irreducible blocks of the Hamiltonian, the level spacings in the limit of large system sizes follow the distribution expected for hermitian random matrices from the Gaussian orthogonal ensemble. We show this by analyzing the distribution of the ratios of consecutive level spacings in this system, its cumulative distribution and quantify the deviations of the distributions using their mean, standard deviation and skewness.

Steady off-diagonal long-range order state in a half-filled dimerized Hubbard chain induced by a resonant pulsed field

We show that a resonant pulsed field can induce a steady superconducting state even in the deep Mott insulating phase of the dimerized Hubbard model. The superconductivity found here in the non-equilibrium steady state is due to the $\eta $-pairing mechanism, characterized by the existence of the off-diagonal long-range order (ODLRO), and is absent in the ground-state phase diagram. The key of the scheme lies in the generation of the field-induced charge density wave (CDW) state that is from the valence bond solid. The dynamics of this state resides in the highly-excited subspace of dimerized Hubbard model and is dominated by a $\eta $-spin ferromagnetic model. The decay of such long-living excitation is suppressed because of energy conservation. We also develop a dynamical method to detect the ODLRO of the non-equilibrium steady state. Our finding demonstrates that the non-equilibrium many-body dynamics induced by the interplay between the resonant external field and electron-electron interaction is an alternative pathway to access a new exotic quantum state, and also provides an alternative mechanism for enhancing superconductivity.

Charge glass in an extended dimer Hubbard model

The charge degrees of freedom in several different organic charge transfer salts display slow or glassy dynamics. In order to gain insight into this behaviour, we obtain the low energy theory for an extended dimer Hubbard model, taking into account the occupations of sites on neighbouring dimers. We take a classical limit of the resulting effective model of coupled spins and dimers and study it using classical Monte Carlo simulations. We find that frustration induced by intra- and inter-dimer interactions leads to glassiness in the charge degress of freedom in the absence of ordering of the spin degrees of freedom. Our results may have relevance to experimental observations of relaxor ferroelectric behaviour in the dynamics of organic charge transfer salts.

Doping-driven resistive collapse of the Mott insulator in a minimal model for VO2

We study the resistive collapse of the Mott insulator state in the dimer Hubbard model. This minimal model has been used to describe the physics of ${\mathrm{VO}}_{2}$, and should be relevant to other strongly correlated materials. It incorporates the physics of correlated dimers and the explicit competition between on-site Coulomb repulsion and magnetic exchange interactions. Our results unveil that between the Mott insulator at half filling and the Fermi liquid metal at high doping there is an intermediate bad metallic phase with exotic features such as a pseudogap, orbital selectivity, and a first-order metal-metal transition. The model is solved within dynamical mean field theory by means of quantum Monte Carlo, which provides the numerically exact solution of the model in the limit of large lattice dimensionality. This model can be considered as a minimal one that captures exotic phenomena associated to the physics of a doped Mott insulator, shading light on their basic physical mechanism.

Imaging the nanoscale phase separation in vanadium dioxide thin films at terahertz frequencies

Vanadium dioxide (VO2) is a material that undergoes an insulator–metal transition upon heating above 340 K. It remains debated as to whether this electronic transition is driven by a corresponding structural transition or by strong electron–electron correlations. Here, we use apertureless scattering near-field optical microscopy to compare nanoscale images of the transition in VO2 thin films acquired at both mid-infrared and terahertz frequencies, using a home-built terahertz near-field microscope. We observe a much more gradual transition when THz frequencies are utilized as a probe, in contrast to the assumptions of a classical first-order phase transition. We discuss these results in light of dynamical mean-field theory calculations of the dimer Hubbard model recently applied to VO2, which account for a continuous temperature dependence of the optical response of the VO2 in the insulating state.

Multiple crossovers and coherent states in a Mott-Peierls insulator

We consider the dimer Hubbard model within Dynamical Mean Field Theory to study the interplay and competition between Mott and Peierls physics. We describe the various metal-insulator transition lines of the phase diagram and the break down of the different solutions that occur along them. We focus on the specific issue of the debated Mott-Peierls insulator crossover and describe the systematic evolution of the electronic structure across the phase diagram. We found that at low intra-dimer hopping the emerging local magnetic moments can unbind above a characteristic singlet temperature $T^*$. Upon increasing the inter-dimer hopping subtle changes occur in the electronic structure. Notably, we find Hubbard bands of a mix character with coherent and incoherent excitations. We argue that this state is relevant for VO$_2$ and its signatures may be observed in spectroscopic studies, and possibly through pump-probe experiments.

Electron-vibrational model for an organic dimer based on cation radicals TTF+ and anion radicals TCNQ−

The electron-vibrational model for an organic dimer proposed in this paper allows one to take into account not only the electron correlation (the organic charge transfer complexes are strongly correlated systems) through the dimerized Hubbard model but also the internal structure of the dimer and each of its monomers by introducing an additional term into the Hamiltonian to describe the interaction between the electrons and the vibrational subsystem. Thus, it provides ample opportunities to minutely describe the polarization and conduction properties of organic dimer systems.

Tomonaga-Luttinger parameters and spin excitations in the dimerized extended Hubbard model

We study the one-dimensional extended Hubbard model with alternating size of the hopping integrals using the density-matrix renormalization group method. We calculate the spin gap, the Tomonaga-Luttinger parameter, and the charge-density-wave order parameter for various dimerizations, interaction strengths, and band fillings. At half band-filling the spin and charge excitations are gapped but these gaps disappear for infinitesimal hole doping. At quarter filling, the umklapp scattering in the half-filled lower Peierls band generates a gap for the charge excitations but the gapless spin excitations can be described in terms of an effective antiferromagnetic Heisenberg model. Beyond a critical strength for the nearest-neighbor interaction, the dimerized extended Hubbard model at quarter filling develops a charge-density-wave ground state. The dimerization and the nearest-neighbor Coulomb interaction strongly reduce the Tomonaga-Luttinger parameter from its value for the bare Hubbard model. We discuss the relevance of our findings for the Bechgaard salts.

Optical conductivity of the one-dimensional dimerized Hubbard model at quarter filling

We investigate the optical conductivity in the Mott insulating phase of the one-dimensional extended Hubbard model with alternating hopping terms (dimerization) at quarter band filling. Optical spectra are calculated for the various parameter regimes using the dynamical density-matrix renormalization group method. The study of limiting cases allows us to explain the various structures found numerically in the optical conductivity of this model. Our calculations show that the dimerization and the nearest-neighbor repulsion determine the main features of the spectrum. The on-site repulsion plays only a secondary role. We discuss the consequences of our results for the theory of the optical conductivity in the Bechgaard salts.

Bosonization of dimerized Hubbard chains

AbstractThe role of Klein factors is investigated for the bosonized Hamiltonian of the dimerized Hubbard model. Contrary to previous approaches we take into account their number changing property, i.e. we do not replace them by Majorana fermions. We show how to treat Klein factors in the framework of the self‐consistent harmonic approximation, both for finite systems and in the thermodynamic limit. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Calculation of Penetration Depth andTcin κ-(ET)2Cu(NCS)2under Pressure

The pressure dependence of the inverse square of the magnetic penetration depth λ -2 in κ-(ET) 2 Cu(NCS) 2 was measured by Larkin et al. [Phys. Rev. B 64 (2001) 144514]. According to the paper, λ -2 behaves differently under low pressure and under high pressure. Under low pressure, the development of λ -2 just below T = T c is rapid compared to the case under high pressure. Moreover, T c in κ-(ET) 2 Cu(NCS) 2 increases under c -axis pressure up to 1 kbar and decreases under higher pressure, while T c decreases monotonically under the hydrostatic pressure, or under the uniaxial pressure parallel to other axes. In order to explain these behaviors, we calculate T c and λ -2 for κ-(ET) 2 Cu(NCS) 2 under pressure. In the calculation we mainly use an effective dimer Hubbard model. In conclusion, the behavior of λ -2 results from three effects: the variation of the bandwidth of quasiparticles, the change of the Fermi surfaces, and the effect of vertex correction. This is a different mechanism from that of λ -2 in cuprates which we observe when the doping varies. Moreover, we explain the increase in T c under the c -axis pressure up to 1 kbar and the decrease in T c over 1 kbar from our calculation. With the increase in the c -axis pressure, two competitive effects with respect to T c appear. One is the approach of the Fermi surface to the antiferromagnetic Brillouin zone boundary, and the other is the suppression of the electron correlation. Under the low c -axis pressure, T c increases since the former effect is dominant. On the other hand, T c decreases since the latter effect is dominant under the high c -axis pressure.

Effects of inter-site repulsion in the one-dimensional dimerized Hubbard model at quarter-filling

To study the metal–insulator (MI) transition of Bechgaad salts, we investigate the one-dimensional (1D) dimerized Hubbard model with the nearest-neighbor Coulomb repulsions at quarter-filling. Density-matrix renormalization group (DMRG) technique is used to obtain the charge gap of this model. Thus, we examine the effect of the nearest-neighbor repulsion on the charge gap. We also investigate the simplified model of quasi-1D organic systems, using the weak-coupling theory and mean-field approximation, and then propose a possible idea for the MI transition.

Marginal Paramagnetic State of a One-Dimensional Half-Filled Alternating Chain in (TTM-TTP)AuI2

(TTM-TTP)AuI 2 (TTM-TTP: 2,5-bis[4,5-bis(methylthio)-1,3-dithiol-2-ylidene]-1,3,4,6-tetrathiapentalene) has a dimerized structure along the donor stacking direction, and shows semiconducting behavior below room temperature. ESR, static magnetic susceptibility, and optical reflectance of this salt have been measured to investigate the spin state and the electronic correlation. The ESR signal has been observed from room temperature to 3 K, and the spin susceptibility shows paramagnetic behavior with a rapid decrease below 10 K. The static magnetic susceptibility is paramagnetic and has an anomaly around 10 K in agreement with the ESR result. The chain axis optical reflectance spectra show clear optical gap in the mid-infrared region. An attempt is undertaken to analyze the optical spectrum by means of the one-dimensional dimerized Hubbard model, which suggests that the on-site Coulomb repulsion, U , is small and the spin polarization is located at the marginal paramagnetic boundary. These results indicate that this compound is not a band-insulator but the Mott insulator with a small spin gap.

Charge and spin gaps in the dimerized Hubbard model

By using the bosonization and renormalization group methods, we have studied the low energy physical properties in the one-dimensional dimerized Hubbard model. The formation of charge and spin gaps is investigated both for the half-filled electron band and away from the half-filled band. The scaling laws of the charge and spin gaps with the dimerization parameter Δ and the repulsive interaction strength U are obtained.

Dimensionality Effects on the Charge Gap in the Dimerized Hubbard Model at Quarter Filling: the Density-Matrix and Perturbative Renormalization-Group Approaches

We study dimensionality effects on the charge gap in the dimerized Hubbard model at quarter filling, with two approaches. First, we examine three chains coupled via the interchain one-particle hopping integral t b , by the density-matrix renormalization-group (DMRG) method. Next, we consider the d =1+e dimensional model, using the perturbative renormalization-group (PRG) method. The dimensionality is controlled through t b and e, respectively. Both approaches lead to the conclusion that, for a finite dimerization ratio, the charge gap decreases as the dimensionality increases.

Spin and charge ordering in the dimerized Hubbard model

We study the effect of a chemically or deformation-induced charge-density wave on the spin-density-wave ground state of the Hubbard model at half-filling. We also consider the effect of a lattice deformation associated with a dimerization of the hopping term, thus introducing a competition with a paramagnetic bond-alternating phase. The slave-boson approach is used as an interpolation scheme to treat the electronic correlations from weak to strong coupling and determine the phase diagram of the model. We also apply our results to describe the neutral-ionic transition in organic mixed-stack donor-acceptor crystals.

Charge Gap of the Quasi-One-Dimensional Organic Conductors: A Density-Matrix Renormalization-Group Study

The Density-matrix renormalization-group (DMRG) technique is used to study the one-dimensional (1D) dimerized Hubbard model at quarter filling. We carry out a precise calculation of the charge gap as a function of the interaction and dimerization strengths and evaluate the interaction strength of the effective 1D Hubbard model at half filling. We also examine the effect of nearest-neighbor repulsion on the charge gap, whereby we evaluate the realistic repulsive strengths for quasi-1D organic compounds.

Spin fluctuation-induced superconductivity in organic compounds

Spin fluctuation-induced superconductivity in quasi-two-dimensional organic compounds such as κ-(BEDT-TTF) 2X is investigated within a fluctuation exchange approximation using a half-filled dimer Hubbard model with right-angled isosceles triangular lattice. The calculated value for T c is in good agreement with experiment and the ( U/ τ)-dependence of T c compares qualitatively well with the observed pressure dependence of T c. The pairing symmetry is of ( x 2− y 2)-type and the energy gap develops with decreasing temperature below T c more rapidly than in the BCS model.

Electronic states of the dimerized Hubbard and t– J models for low-dimensional organic superconductors

Density-matrix-renormalization-group (DMRG) technique and Lanczos diagonalization of small clusters are used to study the one-dimensional dimerized Hubbard model at quarter filling. We present a precise calculation of the charge gap as a function of the interaction and dimerization strengths and discuss the metal–insulator transition of quasi-one-dimensional organic compounds. We also discuss the validity of the reduction of the present model to the single-band Hubbard model at half filling.

Quasi-one-dimensional natures in (Et{sub n}Me{sub 4{minus}n}Z)[Pd(dmit){sub 2}]{sub 2}

We studied one of possible ground states for Pd(dmit) 2 salts in a dimerized two-band Hubbard model. By using a strong-coupling expansion, we obtained an effective dimer model which has a quasi-one-dimensional Fermi surface. In the insulating phase, it leads to the Heisenberg model on an anisotropic triangular lattice. We calculated effective exchange coupling strengths within the second order perturbation theory and found that both ferromagnetic and antiferromagnetic couplings are possible. Similarities to and differences from Ni(dmit) 2 salts are discussed.