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.
We derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a non-interacting quantum-mechanical particle for any hopping. We present analytic results for the DOS corresponding to hopping between nearest and next-nearest neighbors, and also for exponentially decreasing hopping amplitudes. Conversely it is possible to construct a hopping Hamiltonian on the Bethe lattice for any given DOS. These methods are based only on th…
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…
We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-self-intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity.…
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 effect of correlated hopping on the charge and heat transport of strongly correlated particles is studied for the Falicov-Kimball model on the Bethe lattice. Exact solutions for the one particle density of states (DOS) and two particle transport function (the "quasiparticle" scattering time) are derived using dynamical mean field theory. For a wide range of the correlated hopping, the transport function exhibits singularities due to the resonant two-particle contribution, whereas the one particle DOS does not show any anomalous features. By tuning the number of itinerant electrons, so as t…
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 report density-matrix renormalization group calculations of spin gaps in the quarter-filled correlated two-leg rectangular ladder with bond-dimerization along the legs of the ladder. In the small rung-coupling region, dimerization along the leg bonds can lead to large enhancement of the spin gap. Electron-electron interactions further enhance the spin gap, which is nonzero for all values of the rung electron hopping and for arbitrarily small bond-dimerization. Very large spin gaps, as are found experimentally in quarter-filled band organic charge-transfer solids with coupled pairs of quasi-…
Tight binding models like the Hubbard Hamiltonian are most often explored in the context of uniform intersite hopping $t$. The electron-electron interactions, if sufficiently large compared to this translationally invariant $t$, can give rise to ordered magnetic phases and Mott insulator transitions, especially at commensurate filling. The more complex situation of non-uniform $t$ has been studied within a number of situations, perhaps most prominently in multi-band geometries where there is a natural distinction of hopping between orbitals of different degree of overlap. In this paper we expl…
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.
We employ dynamical mean field theory (DMFT) with a Quantum Monte Carlo (QMC) atomic solver to investigate the finite temperature Mott transition in the Hubbard model with the nearest neighbor hopping on a triangular lattice at half-filling. We estimate the value of the critical interaction to be $U_c=12.0 \pm 0.5$ in units of the hopping amplitude $t$ through the evolution of the magnetic moment, spectral function, internal energy and specific heat as the interaction $U$ and temperature $T$ are varied. This work also presents a comparison between DMFT and finite size determinant Quantum Monte…
Theoretical description of anisotropic systems, such as layered superconductors and coupled spin chains, is often a challenge due to the different natures of interactions along different directions. As a model of such a system, we present an analytical study of d-dimensional "nodes" arranged as the vertices of a Bethe lattice, where each node has nonzero spatial dimension and is described by an O(N) quantum rotor model, and there is hopping between neighboring nodes. In the limit of large connectivity on the Bethe lattice, the hopping can be treated by constructing a self-consistent effective …
The two-orbital Hubbard model on a square lattice at quarter filling (electron number per site $n=1$) is investigated by the variational Monte Carlo method. For the variational wave function, we include short-range doublon-holon binding factors. We find that the energy of this wave function is lower than that of the density-density Jastrow wave function partially including long-range correlations used in a previous study. We introduce frustration to the model by the next-nearest-neighbor hopping $t'$ in addition to the nearest-neighbor hopping $t$. For $t'=0$, a ferromagnetic state with stagge…
The extrapolation of small-cluster exact-diagonalization calculations is used to examine the influence of correlated hopping on valence and metal-insulator transitions in the one-dimensional Falicov-Kimball model. It is shown that the ground-state phase diagram as well as the picture of valence and metal-insulator transitions found for the conventional Falicov-Kimball model (without correlated hopping) are strongly changed when the correlated hopping term is added. The effect of correlated hopping is so strong that it can induce the insulator-metal transition, even in the half-filled band case…
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.
We investigate the physical properties of two coupled chains of electrons, with a nearly half-filled band, as a function of the interchain hopping t_\perp and the doping. We show that upon doping, the system undergoes a metal-insulator transition well described by a commensurate-incommensurate transition. By using bosonization and renormalization we determine the full phase diagram of the system, and the physical quantities such as the charge gap. In the commensurate phase two different regions, for which the interchain hopping is relevant and irrelevant exist, leading to a confinement-deconfi…
We investigate the electron density distribution and the stability of stripe phases in the realistic two-band model with hopping elements between e_g orbitals at Ni sites on the square lattice, and compare these results with those obtained for the doubly degenerate Hubbard model with two equivalent orbitals and diagonal hopping. For both models we determine the stability regions of filled and half-filled stripe phases for increasing hole doping x=2-n in the range of x<0.4, using Hartree-Fock approximation for large clusters. In the parameter range relevant to the nickelates, we obtain the most…
We calculate the magnetic phase diagram of the Hubbard model for a Bethe lattice with nearest neighbour (NN) hopping $t_1$ and next nearest neighbour (NNN) hopping $t_2$ in the limit of infinite coordination. We use the amplitude $t_2/t_1$ of the NNN hopping to tune the density of states (DOS) of the non-interacting system from a situation with particle-hole symmetry to an asymmetric one with van-Hove singularities at the lower ($t_2/t_1>0$) respectively upper ($t_2/t_1<0$) band edge for large enough $|t_2/t_1|$. For this strongly asymmetric situation we find rather extended parameter regions …
The 2D half-filled Kondo lattice model with exchange J and nearest neighbor hopping t is considered. It is shown that this model belongs to a class of Hamiltonians for which zero-temperature auxiliary field Monte Carlo methods may be efficiently applied. We compute the staggered moment, spin and quasiparticle gaps on lattice sizes up to 12 X 12. The competition between the RKKY interaction and Kondo effect leads to a continuous quantum phase transition between antiferromagnetic and spin-gaped insulators. This transition occurs at J/t = 1.45 \pm 0.05.
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$_{6+δ}$.
We investigate the ground state phase diagram of the half-filled $t-t^{\prime}$ repulsive Hubbard model in the presence of a staggered ionic potential $Δ$, using the continuum-limit bosonization approach. We find, that with increasing on-site-repulsion $U$, depending on the value of the next-nearest-hopping amplitude $t^{\prime}$, the model shows three different versions of the ground state phase diagram. For $t^{\prime} < t^{\prime}_{\ast}$, the ground state phase diagram consists of the following three insulating phases: Band-Insulator at $U<U_{c}$, Ferroelectric Insulator at $U_{c} < U < U_…
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.
The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory for the Anderson-Falicov-Kimball model with nearest-neighbors and next-nearest-neighbors hopping. The half-filled band is analyzed in terms of the chemical potential of the system using the geometric and arithmetic averages. We also introduce the on-site energies exhibiting a long-range correlated disorder, which generates a system with similar characteristics as the one created by a random independent variable distribution. A decrease in the correlated disorder reduces the extended ph…
For a systematic study of charge degrees of freedom in lattices with geometric frustration, we consider spinless fermions on the checkerboard lattice with nearest-neighbor hopping $t$ and nearest-neighbor repulsion $V$ at quarter-filling. An effective Hamiltonian for the limit $|t|\ll V$ is given to lowest non-vanishing order by the ring exchange ($\sim t^{3}/V^{2}$). We show that the system can equivalently be described by hard-core bosons and map the model to a confining U(1) lattice gauge theory.
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.
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…
Confinement-deconfinement transition in quarter-filled two-coupled chains comprising dimerization, repulsive interactions and interchain hopping has been demonstrated by applying the renormalization group method to the bosonized Hamiltonian. The confinement given by the irrelevant interchain hopping occurs with increasing umklapp scattering which is induced by the dimerization leading to effectively half-filling. It is shown that the transition originates in a competition between a charge gap and the renormalized interchain hopping.
We calculate the Hubbard bands for the half-filled Hubbard model on a Bethe lattice with infinite coordination number up to and including third order in the inverse Hubbard interaction. We employ the Kato--Takahashi perturbation theory to solve the self-consistency equation of the Dynamical Mean-Field Theory analytically for the single-impurity Anderson model in multi-chain geometry. The weight of the secondary Hubbard sub-bands is of fourth order so that the two-chain geometry is sufficient for our study. Even close to the Mott--Hubbard transition, our results for the Mott--Hubbard gap agree …
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…
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 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…
In the present work ferromagnetic ordering in the Hubbard model generalized by taking into account the inter-atomic exchange interaction and correlated hopping in partially filled narrow band is considered. In the case of weak electron-electron interaction the ground state energy and condition of ferromagnetic state realization are found using the Green function technique. The obtained results indicate the important role of correlated hopping.
The f-electron spectral function of the Falicov-Kimball model is calculated via a Keldysh-based many-body formalism originally developed by Brandt and Urbanek. We provide results for both the Bethe lattice and the hypercubic lattice at half filling. Since the numerical computations are quite sensitive to the discretization along the Kadanoff-Baym contour and to the maximum cutoff in time that is employed, we analyze the accuracy of the results using a variety of different moment sum-rules and spectral formulas. We find that the f-electron spectral function has interesting temperature dependenc…
We derive two-loop renormalization-group equations for the half-filled one-dimensional Hubbard chains coupled by the interchain hopping. Our renormalization-group scheme for the quasi-one-dimensional electron system is a natural extension of that for the purely one-dimensional systems in the sense that transverse-momentum dependences are introduced in the g-ological coupling constants and we regard the transverse momentum as a patch index. We develop symmetry arguments for the particle-hole symmetric half-filled Hubbard model and obtain constraints on the g-ological coupling constants by which…
We investigate the finite temperature properties of the half filled Hubbard model in two dimensions, with onsite interaction ($U$), in presence of (frustrating) next nearest neighbor hopping ($t^{\prime}$) using a semiclassical approximation scheme. We show that introduction of $t^{\prime}$ results in a finite temperature pseudogapped (PG) phase that separates the small $U$ Fermi liquid and large $U$ Mott insulator. We map out the PG to normal metal crossover temperature scale ($T^*$) as a function of $U$ and $t^\prime$. We demonstrate that in the PG phase, the quadratic dependence of resistiv…
Finite-temperature T>0 transport properties of integrable and nonintegrable one-dimensional (1D) many-particle quantum systems are rather different, showing in the metallic phases ballistic and diffusive behavior, respectively. The repulsive 1D Hubbard model is an integrable system of wide physical interest. For electronic densities $n\neq1$ it is an ideal conductor, with ballistic charge transport for T larger or equal to 0. In spite that it is solvable by the Bethe ansatz, at $n=1$ its T>0 transport properties are a collective-behavior issue that remains poorly understood. Here we combine th…
We solve a very general two-channel fermion-boson model describing charge transport within some background medium by means of a refined pseudo-site density matrix renormalization group (DMRG) technique. Performing a careful finite-size scaling analysis, we determine the ground-state phase diagram and convincingly prove that the model exhibits a metal-insulator quantum phase transition for the half-filled band case. In order to characterize the metallic and insulating regimes we calculate besides the local particle densities and fermion-boson correlation functions, the kinetic energy, the charg…
Three-coupled chains of quarter-filled Hubbard model with dimerization have been studied for periodic boundary conditions. By use of a renormalization group method, it is found that the interchain hopping is renormalized to zero leading to confinement when charge gap becomes larger than the effective interchain hopping energy. Such a result of confinement is compared with that of two-coupled chains.
The spectral functions of the one-band half-filled 1D Hubbard chain are calculated using the exchange-correlation potential formalism developed recently. The exchange-correlation potential is adopted from the exact potential derived from the Hubbard dimer. Within an approximation in which the full Green function is replaced by a non-interacting one, the spectral functions can be calculated analytically. Despite the simplicity of the approximation, the resulting spectra are in favorable agreement with the more accurate results obtained from the dynamic density-matrix renormalization group metho…
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…
Mechanisms of Mott transitions and dx2-y2-wave superconductivity (SC) are studied in the half-filled-band Hubbard model on square lattices with a diagonal hopping term (t'), using an optimization (or correlated) variational Monte Carlo method. In the trial wave functions, a doublon-holon binding effect is introduced in addition to the onsite Gutzwiller projection. We mainly treat a d-wave singlet state and a projected Fermi sea. In both wave functions, first-order Mott transitions without direct relevance to magnetic orders take place at U=Uc approximately of the bandwidth for arbitrary t'/t. …
The paramagnetic phase diagram of the Hubbard model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping on the Bethe lattice is computed at half-filling and in the weakly doped regime using the self-energy functional approach for dynamical mean-field theory. NNN hopping breaks the particle-hole symmetry and leads to a strong asymmetry of the electron-doped and hole-doped regimes. Phase separation occurs at and near half-filling, and the critical temperature of the Mott transition is strongly suppressed.
The optical properties of the quarter-filled single-band CDW systems have been reexamined in the model with the electron-phonon coupling related to the variations of electron site energies. It appears that the indirect, electron-mediated coupling between phase phonons and external electromagnetic fields vanishes for symmetry reasons, at variance with the infrared selection rules used in the generally accepted microscopic theory. It is shown that the phase phonon modes and the electric fields couple directly, with the coupling constant proportional to the magnitude of the charge-density wave. T…
We have studied spin density wave (SDW) phase transitions in dimerized quarter-filled Hubbard chains weakly coupled via interchain one-particle hopping, $t_{b0}$. It is shown that there exists a critical value of $t_{b0}$, $t_{b}^\ast$, between the incoherent metal regime ($t_{b0}<t_{b}^\ast$) and the Fermi liquid regime ($t_{b0}>t_{b}^\ast$) in the metallic phase above the SDW transition temperature. By using the 2-loop perturbative renormalization-group approach together with the random-phase-approximation, we propose a SDW phase diagram covering both of the regimes. The SDW phase transition…
We study the phase diagram of spinless fermions with nearest and next-nearest-neighbor interactions in one dimension utilizing the (finite-size) density-matrix renormalization group (DMRG) method. The competition between nearest and next-nearest-neighbor interactions and nearest-neighbor hopping generates four phases in this model: two charge-density-wave insulators, a Luttinger liquid phase, and a bond-order phase. We use finite-size scaling of the gap and various structure factors to determine the phase diagram.
We report a large-scale density-matrix renormalization group study of the lightly doped Hubbard model on 4-leg cylinders at hole doping concentration $δ=12.5\%$. By keeping a large number of states for long system sizes, we are able to reveal a delicate interplay between superconductivity and charge and spin density wave orders tunable via next-nearest neighbor hopping t'. For finite t', the ground state is consistent with that of a Luther-Emery liquid, having `half-filled' charge stripes with power-law superconducting and charge-density-wave correlations of wave-length $λ=1/2δ$, but short-ran…
We study the quantum phase diagram of spinful fermions on kagome lattice with half-filled lowest flat bands. To understand the competition between magnetism, flat band frustration, and repulsive interactions, we adopt an extended $t$-$J$ model, where the hopping energy $t$, antiferromagnetic Heisenberg interaction $J$, and short-range neighboring Hubbard interaction $V$ are considered. In the weak $J$ regime, we identify a fully spin-polarized phase, which can further support the spontaneous Chern insulating phase driven by the short-range repulsive interaction. This phase still emerges with i…
The half-filled ground state of the Hubbard model in one dimension is studied by Kondo-lattice theory. Because of the Kondo effect, any insulating ground state with a complete gap open is unstable in the presence of an infinitesimal perturbation. This fact casts doubt on the claim by E. H. Lieb and F. Y. Wu, Phys. Rev. Lett. 20, 1445 (1968) that the half-filled ground state is the Mott insulator. Though the claim is based on a rigorous result given by the Bethe-ansatz solution, the rigorous result is simply a necessary condition for the ground state being an insulator.
We investigate the ground-state phase diagram of the quarter-filled Hubbard ladder with nearest-neighbor Coulomb repulsion V using the Density Matrix Renormalization Group technique. The ground-state is homogeneous at small V, a ``checkerboard'' charge--ordered insulator at large V and not too small on-site Coulomb repulsion U, and is phase-separated for moderate or large V and small U. The zero-temperature transition between the homogeneous and the charge-ordered phase is found to be second order. In both the homogeneous and the charge-ordered phases the existence of a spin gap mainly depends…
The ground state of the Hubbard model with nearest-neighbor hopping on the square lattice at half filling is known to be that of an antiferromagnetic (AFM) band insulator for any on-site repulsion. At finite temperature, the absence of long-range order makes the question of how the interaction-driven insulator is realized nontrivial. We address this problem with controlled accuracy in the thermodynamic limit using self-energy diagrammatic determinant Monte Carlo and dynamical cluster approximation methods and show that development of long-range AFM correlations drives an extended crossover fro…
The equation for the electron Green's function of the fermionic Hubbard model, derived using the strong coupling diagram technique, is solved self-consistently for the near-neighbor form of the kinetic energy and for half-filling. In this case the Mott transition occurs at the Hubbard repulsion $U_c\approx 6.96t$, where $t$ is the hopping constant. The calculated spectral functions, density of states and momentum distribution are compared with results of Monte Carlo simulations. A satisfactory agreement was found for $U>U_c$ and for temperatures, at which magnetic ordering and spin correlation…
We study the single-particle properties of quarter-filled ladder systems such as sodium vanadate 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 C-DMFT and LDA 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…
Effects of the electron-electron umklapp process on dimensional crossovers caused by the interchain one-particle hopping, $t_{\perp}$, in a weakly-coupled half-filled chain system have been studied, based on the perturbative renormalization-group approach. The variance of $t_\perp$ and the umklapp process under scaling is taken into account. We found that the intrachain umklapp process causes a finite crossover value of $t_\perp$, $t_{\perp cr}$. For $t_{\perp}<t_{\perp c}$, as the temperature decreases, the system undergoes a crossesover from the Tomonaga-Luttinger (TL) liquid to an incipient…
