Quarter-filled System Research Articles

Ground-State Properties of the Frustrated 2D Quarter-Filled Hubbard Model

The Hubbard model extended by next-nearest-neighbor (NNN) hopping t′ at quarter filling has been investigated numerically using exact diagonalization technique on a small cluster. We report the role of frustration (NNN hopping) on the ground-state properties of the system. The effects of both positive and negative t′ are considered. Results show that a short range antiferromagnetic order is present in the system, which is favored (suppressed) by negative (positive) t′. It appears that electron-electron correlation decreases with NNN hopping interaction. Inclusion of t′ facilitates electron hopping. Though pairing in the extended s-wave channel is dominant for quarter-filled unfrustrated system, d-wave pairing becomes dominant with the inclusion of negative t′.

Orbital order, metal-insulator transition, and magnetoresistance effect in the two-orbital Hubbard model

We study the effects of temperature and magnetic field on a two-orbital Hubbard model within dynamical mean field theory. We focus on the quarter filled system, which is a special point in the phase diagram due to orbital degeneracy. At this particular filling the model exhibits two different long-range order mechanisms, namely orbital order and ferromagnetism. Both can cooperate but do not rely on each other's presence, creating a rich phase diagram. Particularly, in the vicinity of the phase transition to an orbitally ordered ferromagnetic state, we observe a strong magnetoresistance effect. Besides the low temperature phase transitions, we also observe a crossover between a paramagnetic insulating and a paramagnetic metallic state for increasing Hund's coupling at high temperatures.

Finite-Temperature Phase Diagram of Quasi-One-Dimensional Molecular Conductors: Quantum Monte Carlo Study

Finite-temperature phase transitions in quasi-one-dimensional quarter-filled systems are investigated by the extended Hubbard model with electron-lattice coupling. Using a quantum Monte Carlo method combined with the inter-chain mean-field approximation, we clarify competing and coexisting behaviors among charge ordering, dimer Mott, and spin-Peierls states. It is pointed out that an anharmonicity of lattice distortions plays an important role in multi-critical behaviors. The results are compared with experimental data for quasi-one-dimensional molecular conductors such as DCNQI and TMTTF compounds.

Charge ordering and magnetism in quarter-filled Hubbard-Holstein model

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 ${\text{LaAlO}}_{3}$ and ${\text{SrTiO}}_{3}$, where half-electron per unit cell is transferred to the ${\text{TiO}}_{2}$ layer as a consequence of the polar discontinuity at the interface. In addition to presenting the overall phase diagrams, we identify an interesting charge-ordered antiferromagnetic phase for $n=0.5$, which was also reported recently in the ab initio study of the ${\text{LaAlO}}_{3}{\text{-SrTiO}}_{3}$ interface.

Quantum critical transition from charge-ordered to superconducting state in the negative-Uextended Hubbard model on a triangular lattice

We demonstrate a robust frustration-driven charge order to superconductivity transition in the half-filled negative-$U$ extended Hubbard model. Superconductivity extends over a broad region of the parameter space. We argue that the model provides the correct insight to understanding unconventional superconductivity in the organic charge-transfer solids and other quarter-filled systems.

Single-particle spectral function of quarter-filled ladder systems

We study the single-particle properties of quarter-filled ladder systems such as ${\ensuremath{\alpha}}^{\ensuremath{'}}\text{\ensuremath{-}}\mathrm{Na}{\mathrm{V}}_{2}{\mathrm{O}}_{5}$ by means of a recently developed generalization of the variational cluster perturbation theory to extended Hubbard models. We find a homogeneous antiferromagnetic insulating phase for nearest-neighbor repulsions smaller than a critical value, without any metallic phase for small repulsions. Different from cluster dynamical mean-field theory and local density approximation considerations, the inclusion of diagonal hopping within a ladder has little effect on the bonding bands, while flattening and shifting the antibonding bands. In the low-temperature charge-ordered phase, the spectrum depends on whether the ordering is driven by the Coulomb repulsion or by the coupling to a static lattice distortion. The small change of the experimentally observed gap upon charge ordering implies that the lattice coupling plays an important role in this ordering. Interladder coupling is straightforward to include within our method. We show that it has only a minor effect on the spectral function. The numerically calculated spectra show good agreement with experimental angle-resolved photoemission data.

Spin exchange and superconductivity in at−J′−Vmodel for two-dimensional quarter-filled systems

The effect of antiferromagnetic spin fluctuations on two-dimensional quarter-filled systems is studied theoretically. An effective $t-J'-V$ model on a square lattice which accounts for checkerboard charge fluctuations and next-nearest-neighbors antiferromagnetic spin fluctuations is considered. From calculations based on large-N theory on this model it is found that the exchange interaction, $J'$, increases the attraction between electrons in the d$_{xy}$ channel only, so that both charge and spin fluctuations work cooperatively to produce d$_{xy}$ pairing.

Quantum melting of charge order due to frustration in two-dimensional quarter-filled systems

The effect of geometrical frustration in a two-dimensional 1/4-filled strongly correlated electron system is studied theoretically, motivated by layered organic molecular crystals. An extended Hubbard model on the square lattice is considered, with competing nearest neighbor Coulomb interaction, V, and that of next-nearest neighbor along one of the diagonals, V', which favor different charge ordered states. Based on exact diagonalization calculations, we find a metallic phase stabilized over a broad window at V' ~ V even for large Coulomb repulsion strengths as a result of frustrating the charge ordered states. Slightly modifying the lattice geometry relevant to the actual organic compounds does not alter the results, suggesting that this `quantum melting' of charge order is a robust feature of frustrated strongly correlated 1/4-filled systems.

Quantum Monte Carlo Study of Insulating State in NaV2O5.

Abstract Quantum Monte Carlo (QMC) methods are being increasingly used as complements to Hartree–Fock (HF) methods for computing the electronic structure of molecules and materials. We investigate the nature of the insulating state driven by electronic correlations in the ladder compound NaV 2 O 5 ; considered as a quarter-filled system. We use an extended Hubbard model (EHM) to study the role of on-site and inter-site Coulomb interaction. It is found that the insulating state in the charge-disordered phase of this compound take origin from the transfer of spectral density and dynamical fluctuations. Our calculation allows us also, to understand the origin of the insulating states above T C and to estimate the relative importance of various physical mechanisms responsible for the gap formation.

Quantum Monte Carlo study of insulating state in NaV 2O 5

Quantum Monte Carlo (QMC) methods are being increasingly used as complements to Hartree–Fock (HF) methods for computing the electronic structure of molecules and materials. We investigate the nature of the insulating state driven by electronic correlations in the ladder compound NaV 2O 5; considered as a quarter-filled system. We use an extended Hubbard model (EHM) to study the role of on-site and inter-site Coulomb interaction. It is found that the insulating state in the charge-disordered phase of this compound take origin from the transfer of spectral density and dynamical fluctuations. Our calculation allows us also, to understand the origin of the insulating states above T C and to estimate the relative importance of various physical mechanisms responsible for the gap formation.

Ferromagnetism in the one-dimensional Hubbard model with orbital degeneracy: From low to high electron density

We studied ferromagnetism in the one-dimensional Hubbard model with doubly degenerate atomic orbitals by means of the density-matrix renormalization-group method and obtained the ground-state phase diagrams. It was found that ferromagnetism is stable from low to high (0< n < 1.75) electron density when the interactions are sufficiently strong. Quasi-long-range order of triplet superconductivity coexists with the ferromagnetic order for a strong Hund coupling region, where the inter-orbital interaction U'-J is attractive. At quarter-filling (n=1), the insulating ferromagnetic state appears accompanying orbital quasi-long-range order. For low densities (n<1), ferromagnetism occurs owing to the ferromagnetic exchange interaction caused by virtual hoppings of electrons, the same as in the quarter-filled system. This comes from separation of the charge and spin-orbital degrees of freedom in the strong coupling limit. This ferromagnetism is fragile against variation of band structure. For high densities (n>1), the phase diagram of the ferromagnetic phase is similar to that obtained in infinite dimensions. In this case, the double exchange mechanism is operative to stabilize the ferromagnetic order and this long-range order is robust against variation of the band-dispersion. A partially polarized state appears in the density region 1.68<n<1.75 and phase separation occurs for n just below the half-filling (n=2).

Study of the phase transitions of (DI-DCNQI) 2X using vibronic and vibrational spectra

A model for the vibrational and vibronic features of the infrared spectra of a quarter-filled system is reported and shown to be able to characterise the BOW and CDW ground state of these compounds. The infrared spectra of (DI-DCNQI) 2 Ag and of the corresponding compounds with Li and Cu are analysed. In particular for the Ag compound one finds that a 4k F BOW begins to develop from room temperature and that a CDW develops below 200 K. The understanding of the periodicity of the low temperature BCDW necessitates further investigations.

Magnetic property of MMX chains as dimerized quarter-filled systems

We study ground state phase diagrams for the MMX chains, using a one-dimensional dimerized 3 4 -filled extended Hubbard–Peierls model with site diagonal and off-diagonal electron–lattice interactions. The ground states are obtained both in the Hartree–Fock approximation and by the exact diagonalization. We discuss magnetic properties of the MMX chains.

Two Kinds of the Coexistent States in One-Dimensional Quarter-Filled Systems under Magnetic Fields and Temperatures

The coexistent state of the spin density wave (SDW) and the charge density wave (CDW) in the one-dimensional quarter-filled system and with the Coulomb interaction up to the next-nearest sites under magnetic fields is studied. It is found that, in the coexistent state of $2k_{\rm F}$-SDW and $2k_{\rm F}$-CDW, the charge order is suppressed and $2k_{\rm F}$-SDW changes to $2k_{\rm F}$-SDW having the different alignment of spin under high magnetic fields, whereas, in the coexistent state of $2k_{\rm F}$-SDW and $4k_{\rm F}$-CDW, $4k_{\rm F}$-CDW still remains and $2k_{\rm F}$-SDW is suppressed. The critical temperature of the charge order is higher than that of the spin order when the inter-site Coulomb interaction is strong. These will be observed in experiments such as the X-ray scattering measurement and NMR.

Density-matrix renormalization-group study of the spin gap in a one-dimensional Hubbard model: Effect of the distant transfer and exchange coupling

The spin gap of a one-dimensional repulsive Hubbard model is numerically calculated with the density matrix renormalization group, with a special emphasis on the effect of a next-nearest neighbor hopping (t') and the nearest-neighbor ferromagnetic exchange (J) interaction. At half-filling, a significant spin gap opens if |t'| \simeq |t| and J=0, in agreement with the weak coupling theory, while the gap is strongly suppressed by the introduction of J. On the other hand, the quarter-filled system has very small spin gaps regardless of the values of t' and J. Implications for the CuO_2 chain in Sr_{14}Cu_{24}O_{41} and related materials are discussed.

Impurity in a Luttinger liquid away from half-filling: A numerical study

Conformal field theory gives quite detailed predictions for the low energy spectrum and scaling exponents of a massless Luttinger liquid at generic filling in the presence of an impurity. While these predictions were verified for half-filled systems, there was till now no analysis away from this particular filling. Here, we fill in this gap by numerically investigating a quarter-filled system using the density matrix renormalization group technique. Our results confirm conformal field theory predictions, and suggest that they are indeed valid for arbitrary fillings.

Exact result on the Mott transition in a two-dimensional model of strongly correlated electrons.

We study the properties of a quarter-filled system of electrons on a square lattice interacting through a local repulsion $U$ and a nearest-neighbour repulsion $V$ in the limit $V=+\infty$. We identify the ground-state for $U$ large enough and show that domain walls appear below a critical value $U_c=4t/\pi$. We argue that this corresponds to a metal-insulator transition due to Mott localization.

Peierls instabilities in one-dimensional systems with Jahn-Teller-active monomers

A one-dimensional system is investigated which consists of monomers with Jahn-Teller-active vibrational coordinates. Peierls distortions in the ground states of the half- and quarter-filled systems are studied as a function of the electron-lattice and Jahn-Teller coupling constants. For both degrees of filling and for all the values of the coupling constants the band structure of the ground state is doubly degenerate. The interrelation is discussed between the present system and systems where the active internal degrees of freedom are not of the Jahn-Teller type.

Dimerization, vibronic structures, and optical gaps in the (TMTTF) 2X and (TMTSF) 2X salts

We have analyzed the infrared properties of a 1-D dimerized tight binding system with linear coupling to one inter- and one intramolecular phonon. The infrared conductivity has been calculated for a quarter-filled system both in the small U and large U limits. A suitable choice of the model parameters allows the comparison with the experimental infrared conductivity of representative (TMTTF) 2X and (TMTSF) 2X salts. The reseults indicate that the infrared properties are quite sensitive to the effects of the gap open by the chain dimerization. This can only be explained if a large on-site correlation U is included. Previously noted correlations between d.c. conductivity and infrared properties are easily explained with the interpretative scheme suggested here.

Fractionally Charged States in Quarter-Filled Electron-Phonon Systems

Various fractionally charged states in nearly quarter-filled one-dimensional electron-phonon systems are numerically investigated for Su-Schrieffer-Heeger's model. Three types of solitons are obtained depending on the excess electron number δ n = N e - N /2 and spin s with N and N e the total numbers of lattice sites and electrons; they may be called phase solitons, charged amplitude solitons and a neutral amplitude soliton for (δ n , s ) = (±1/2, 0), (±1/2, 1/2) and (0, 1/2), respectively. The states for the other δ n 's are found to consist of proper combinations of the above solitons well separated from one another. Electronic levels corresponding to localized states associated with the solitons exist not only within the gap between the conduction and valence bands but also below the valence band. Creation energies and widths of the solitons are calculated for various coupling constants.