The extended Hubbard model in an anisotropic triangular lattice is analyzed at quarter filling by the functional renormalization group (fRG) approach. We obtain the finite temperature phase diagram in the plane of nearest inter-site Coulomb interaction Vp and next-nearest Coulomb interaction Vc. When Vp ? Vc, charge order does not occur down to the low temperature of 0.1tp, where the tp is the electron transfer between the nearest neighbor sites. We interpret the result using the random-phase approximation(RPA).
The zero-frequency wave-vector-dependent charge- and spin-density susceptibilities for a quarter-filled-band extended Hubbard model are calculated with the use of a Monte Carlo technique. Results for a variety of different temperatures are given. Coulomb interactions are found to suppress the
2pF charge-density response and enhance the
2pF spin-density response. While a strictly on-site Coulomb interaction gives rise to only a weak
4pF structure in the charge-density response, longer-range Coulomb interactions such as the near-neighbor interaction
V in the extended Hubbard model can produce a singularity at
4pF. In addition to these susceptibilities, both the charge and spin structure factors are calculated, as well as two-particle, two-hole correlation functions. We also show some results for the ground-state energy, magnetic susceptibility, and specific heat of the Hubbard model. The relationship of the results obtained from our Monte Carlo simulations to various limiting exact results as well as to the well-known weak coupling renormalization-group predictions are discussed.
Several new classes of compounds can be modeled in first approximation by electrons on the triangular lattice that interact through on-site repulsion
U as well as nearest-neighbor repulsion
V. This extended Hubbard model on a triangular lattice has been studied mostly in the strong coupling limit for only a few types of instabilities. Using the extended two-particle self-consistent approach (ETPSC), that is valid at weak to intermediate coupling, we present an unbiased study of the density and interaction dependent crossover diagram for spin- and charge-density wave instabilities of the normal state at arbitrary wave vector. When
U dominates over
V and electron filling is large, instabilities are chiefly in the spin sector and are controlled mostly by Fermi surface properties. Increasing
V eventually leads to charge instabilities. In the latter case, it is mostly the wave vector dependence of the vertex that determines the wave vector of the instability rather than Fermi surface properties. At small filling, nontrivial instabilities appear only beyond the weak coupling limit. There again, charge-density wave instabilities are favored over a wide range of dopings by large
V at wave vectors corresponding to $\sqrt{(3)}\ifmmode\times\else\texttimes\fi{}\sqrt{(3)}$ superlattice in real space. Commensurate fillings do not play a special role for this instability. Increasing
U leads to competition with ferromagnetism. At negative values of
U or
V, neglecting superconducting fluctuations, one finds that charge instabilities are favored. In general, the crossover diagram presents a rich variety of instabilities. We also show that thermal charge-density wave fluctuations in the renormalized-classical regime can open a pseudogap in the single-particle spectral weight, just as spin or superconducting fluctuations.
A formalism based on the fermionic functional-renormalization-group approach to interacting electron models defined on a lattice is presented. One-loop flow equations for the coupling constants and susceptibilities in the particle-particle and particle-hole channels are derived in weak-coupling conditions. It is shown that lattice effects manifest themselves through the curvature of the spectrum and the dependence of the coupling constants on momenta. This method is then applied to the one-dimensional extended Hubbard model; we thoroughly discuss the evolution of the phase diagram, and in particular the fate of the bond-centered charge-density-wave phase, as the system is doped away from half-filling. Our findings are compared to the predictions of the field-theory continuum limit and available numerical results.
A chiral spin liquid (CSL) phase has been recently reported in the Hubbard model on a triangular lattice. It emerges in an intermediate coupling regime at half-filling, which is sandwiched between a ${120}^{\ensuremath{\circ}}$ antiferromagnetic (AFM) phase and a metallic phase as a function of on-site repulsion
U. In this work, we examine the mechanism of the CSL and complex phase diagram via analytic analysis and numerical density matrix renormalization group (DMRG) method. First, we identify an exact Berry-phase-like sign structure in the partition function of the model at arbitrary
U, which is originated from the Fermi sign structure at
U=0.The spin and charge degrees of freedom are generally entangled via a singular phase string in such a many-body sign structure. In the large-
U limit, the suppression of the charge fluctuation at half-filling can render the phase string ineffective, resulting in the AFM order. However, if one precisely switches off such a phase string in the DMRG calculation, the ${120}^{\ensuremath{\circ}}$ AFM is shown to survive all the way down to a much weaker
U without the emergence of the CSL and metallic phases. It indicates that the phase-string sign structure plays the key role to mediate the mutual interaction between the charge and spin fluctuations, which results in the CSL and metallic phases at finite
U. General implications for the Mott physics in the Hubbard model will also be discussed.
A chiral spin liquid (CSL) phase has been recently reported in the Hubbard model on a triangular lattice at half-filling. It emerges in an intermediate coupling regime, which is sandwiched between a
120∘ antiferromagnetic (AFM) phase and a metallic phase as a function of on-site repulsion
U. In this work, we examine how the charge fluctuation may cause the CSL and complex phase diagram. We first identify an exact sign structure of the model at arbitrary temperature, sample size, and doping, which is reduced from the original Fermi exchange signs of the electrons by finite
U. In particular, the spin and charge degrees of freedom are generally entangled via the phase-string in the sign structure. By precisely switching off such a phase-string, the CSL phase is shown to disappear, with only the
120∘ AFM order remaining down to weak
U by a density matrix renormalization group calculation. Here the charge fluctuation is effectively decoupled from the AFM background, which is a
120∘ AFM order due to a geometric Berry phase in the sign structure of the triangular lattice. General implications for the Mott physics will also be discussed.