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Physical review. B, Condensed matter

Ground state of a chemically modulated Hubbard chain at half filling

Sanjay Gupta, Shreekantha Sil, Bibhas Bhattacharyya

Published Mar 12, 2001• 16 citations
Publisher

Abstract

We have studied the Hubbard chain with a periodic variation of the site potential for the half-filled band by using a real space renormalization group (RG) method complemented by a mean-field analysis. The ground state phase diagram shows a transition between a charge density wave (CDW) and a spin density wave (SDW). The energy gap and the local moment, as obtained from the RG, clearly identify the phase transition in agreement with the RG flow pattern. Within the mean-field approximation (MFA) the charge and spin order parameters are calculated to trace out the transition. The phase diagram obtained by the RG calculation shows excellent agreement with that obtained by the MFA especially in the weak- to intermediate-coupling region. We have also calculated the Drude weight (within the MFA) to analyze the conductivity of such a chain of finite length. The Drude weight also captures some interesting features of the competition between the SDW and the CDW.

DOI
10.1103/physrevb.63.125113

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We have studied the Hubbard chain with a periodic variation of the site potential for the half-filled band by using a real space renormalization group (RG) method complemented by a mean-field analysis. The ground state phase diagram shows a transition between a charge density wave (CDW) and a spin density wave (SDW). The energy gap and the local moment, as obtained from the RG, clearly identify the phase transition in agreement with the RG flow pattern. Within the mean-field approximation (MFA) the charge and spin order parameters are calculated to trace out the transition. The phase diagram obtained by the RG calculation shows excellent agreement with that obtained by the MFA especially in the weak- to intermediate-coupling region. We have also calculated the Drude weight (within the MFA) to analyze the conductivity of such a chain of finite length. The Drude weight also captures some interesting features of the competition between the SDW and the CDW.
We reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the weak-coupling renormalization-group approach ( g-ology) to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.
We have studied a one-dimensional Hubbard superlattice with different Coulomb correlations at alternating sites for a half-filled band. Mean field calculations based on the Hartree-Fock approximation together with a real space renormalization group technique were used to study the ground state of the system. The phase diagrams obtained in these approaches agree with each other from the weak to the intermediate coupling regime. The mean field results show very quick convergence with system size. The renormalization group results indicate a spatial modulation of local moments that was identified in some previous work. Also we have studied the magnetoconductance of such superlattices which reveals several interesting points.
We have investigated the ground-state phase diagram of the one-dimensional Hubbard model with alternating chemical potentials at half-filling by bosonization technique and the Gaussian wave functional method. We calculate variations of the charge density wave (CDW) and the spin density wave (SDW) gaps, ad well as their classical trajectory c,s with increasing on-site Coulomb repoulsion potential. For the fixed potential, it is found that the transition from the band insulator (BI) to the spontaneously dimerized insulator (SDI) is of the Ising type, at which charge gap vanishes, while the transition from SDI to the Mott insulator (MI) is of the KT type.
It has been well established that in both the weak- and strong-coupling limits, the phase transition from a spin-density wave (SDW) to a charge-density wave (CDW) in the half-filled extended-Hubbard model occurs precisely at the ratio U/Vc=2,{U/V}_{c}=2,U/Vc​=2, where U and V are the on-site and intersite electron-electron interactions, respectively. However, a recent density-matrix renormalization group (DMRG) study and a previous Monte Carlo simulation jointly suggest a picture that challenges the well-established weak-coupling result. Here, a careful calculation shows such a picture is questionable. In particular, it clarifies the DMRG result, even with a moderate number of states kept in the density matrix, agrees with both the weak- and strong-coupling findings, and predicts a CDW/SDW phase boundary smoothly links those two coupling limits. Possible sources of these previous failures are discussed.
The square-lattice extended Hubbard model at half filling is studied by a perturbation scheme. By taking into account the ground state of the mean-field theory as a reference state, the scheme treats the collective fluctuations beyond the mean field as the predominant perturbation. The system at ground state can be a spin-density wave (SDW) or a charge-density wave (CDW) depending on the relative strengths of the on-site electron interaction and the nearest-neighbor interaction. The excitation modes above the ground state are analyzed through diagonalizing an effective Hamiltonian. The energy spectra and the wave functions are self-consistently given by the formalism. By comparing the ground-state energies, we investigate the SDW-CDW transition.