Quantum antiferromagnetic (AF) fluctuations that promote the charge-density-wave (CDW)-AF state phase transition in the one-dimensional (1D) extended Hubbard model are clarified for the strong correlation regime. It is clearly shown that the CDW wave function contains quantum fluctuations due to the AF domains near the phase boundary. Though the size of these AF domains stays finite, its density to the system size becomes asymptotically zero in the infinite-size limit. This indicates the quantum decoherence, or the first order phase transition between the CDW and AF state. On the other hand, the survived AF domains would naturally evolve into the quantum nucleation that triggers the CDW-AF state phase transition.
Quantum antiferromagnetic (AF) fluctuations that promote the charge-density-wave (CDW)-AF state phase transition in the one-dimensional (1D) extended Hubbard model are clarified for the strong correlation regime. It is clearly shown that the CDW wave function contains quantum fluctuations due to the AF domains near the phase boundary. Though the size of these AF domains stays finite, its density to the system size becomes asymptotically zero in the infinite-size limit. This indicates the quantum decoherence, or the first order phase transition between the CDW and AF state. On the other hand, the survived AF domains would naturally evolve into the quantum nucleation that triggers the CDW-AF state phase transition.
The charge-density-wave (CDW)--spin-density-wave (SDW) phase transition of the one-dimensional extended Hubbard model is investigated in the strong correlation regime, from the viewpoint of the quantum coherence or decoherence of the two correlated states. In the finite-size system, the CDW wave function, near the phase boundary, has the significant quantum fluctuations due to the SDW domains. The superposition of these SDW domains leads to the quantum coherence between the CDW and SDW wave functions. However, the scaling analysis shows that the density of the SDW fluctuations becomes asymptotically zero in the infinite-size limit, which indicates the decoherence of the two states in the bulk phase transition.
The effect of quantum lattice fluctuations is investigated in a half-filled one-dimensional Peierls-Hubbard model. The nonadiabatic effects due to finite phonon frequency \ensuremath{\omega} are treated by introducing the polaronic transformation and the squeezed-phonon state. The electronic correlations are treated by means of a modified Gutzwiller approach and a unified description for the long-range charge-density-wave (CDW) ordering state and the short-range antiferromagnetic correlated state has been developed. The main result is a rather good description of the continuous variation of the dimerization as functions of the Hubbard U and \ensuremath{\omega} is given, which is in good agreement with that of the numerical simulations. The results of the squeezed-polaron theory are shown to be better than those of the ordinary polaron theory. A continuous phase transition is found between the long-range CDW ordering state and the short-range antiferromagnetic correlated state with a transition point different from the prediction of the Hartree-Fock decoupling. The effect of quantum lattice fluctuations on the transition point is also discussed.
We use a stochastic series-expansion quantum Monte Carlo method to study the phase diagram of the one-dimensional extended Hubbard model at half-filling for small to intermediate values of the on-site U and nearest-neighbor V repulsions. We confirm the existence of a novel, long-range-ordered bond-order-wave (BOW) phase recently predicted by Nakamura [J. Phys. Soc. Jpn. 68, 3123 (1999)] in a small region of the parameter space between the familiar charge-density-wave (CDW) state for $V\ensuremath{\gtrsim}U/2$ and the state with dominant spin-density-wave (SDW) fluctuations for $V\ensuremath{\lesssim}U/2.$ We discuss the nature of the transitions among these states and evaluate some of the critical exponents. Further, we determine accurately the position of the multicritical point, ${(U}_{m}{,V}_{m})=(4.7\ifmmode\pm\else\textpm\fi{}0.1,2.51\ifmmode\pm\else\textpm\fi{}0.04)$ (in energy units where the hopping integral is normalized to unity), above which the two continuous SDW-BOW-CDW transitions are replaced by one discontinuous (first-order) direct SDW-CDW transition. We also discuss the evolution of the CDW and BOW states upon hole doping. We find that in both cases the ground state is a Luther-Emery liquid, i.e., the spin gap remains but the charge gap existing at half-filling is immediately closed upon doping. The charge and bond-order correlations decay with distance r as ${r}^{\ensuremath{-}{K}_{\ensuremath{\rho}}},$ where ${K}_{\ensuremath{\rho}}$ is approximately 0.5 for the parameters we have considered. We also discuss advantages of using parallel tempering (or exchange Monte Carlo)---an extended ensemble method that we here combine with quantum Monte Carlo---in studies of quantum phase transitions.
Antiferromagnetism, charge density wave, and d-wave superconductivity in the t-J-U-V model of correlated electrons: Role of direct Coulomb interactions
We study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase and show it appears only above some critical values of V and in a limited hole doping range δ. The effect of the term V on SC and AF phases is that a strong interaction suppresses SC altogether, whereas the AF order is not significantly influenced by its presence. Calculations for the case of pure SC phase have been also carried out within an extended approach, the extended approach, the diagrammatic expansion for the Gutzwiller wave function (DE-GWF) in order to analyze influence of the higher-order correlations onto this phase beyond the renormalized mean field approach. In the Appendices we discuss, the specific ambiguity of the choice of the Gutzwiller renormalization factors within the SGA when either AF or CDW orders are considered.
We study extended Hubbard and Peierls-Hubbard models with up to N=10 sites and half-filled bands with modified boundary conditions. For the extended Hubbard model, the finite-size dependence of the transition from the charge-density-wave regime (CDW) to the spin-density-wave (SDW) regime and of the condensation transition is critically examined, clarifying some previous results. For the Peierls-Hubbard model and N\ensuremath{\le}10 with modified periodic boundary conditions, we always see a decrease of dimerization with U. Extrapolating these results to infinite N, we find that dimerization is enhanced by U for small electron-phonon coupling \ensuremath{\alpha}\ifmmode \tilde{}\else \~{}\fi{}0.75, whereas it decreases with U for 0.75\ensuremath{\le}1. By extending this model by a nearest-neighbor repulsion V, the amplitude of dimerization reaches a maximum at the same value U\ensuremath{\le}2V, where the CDW-to-SDW transition occurs in the extended Hubbard model.
Strongly correlated materials exhibit some of the most complex and technologically useful phenomena in condensed matter. We use the world line and determinant quantum Monte Carlo techniques to explore the phases of the Hubbard Hamiltonian, a model describing strong interactions, in a number of different contexts. We first consider the spin, charge, and bond order correlations of the one-dimensional extended fermion Hubbard model in the presence of a coupling to the lattice. A static alternating lattice distortion leads to enhanced charge density wave correlations at the expense of antiferromagnetic order. When the lattice degrees of freedom are dynamic, we show that a similar effect occurs even though the charge asymmetry must arise spontaneously. Although the evolution of the total energy with lattice coupling is smooth, the individual components exhibit sharp crossovers at the phase boundaries. Finally, we observe a tendency for bond order in the region between the charge and spin density wave phases. Second, we examine mixtures of bosons and fermions in one-dimensional optical lattices. We evaluate the density profiles and bosonic visibility [special characters omitted] resolving the discrepancy between theory and experiment by identifying parameter regimes where [special characters omitted] is reduced and increased. We present a simple qualitative picture of the different response to the fermion admixture in terms of the superfluid and Mott-insulating domains before and after the fermions are included. Finally, we show that [special characters omitted] exhibits kinks which are tied to the domain evolution present in the pure bosonic case, and also additional structure arising from the formation of boson-fermion molecules, a prediction for future experiments. Third, we report large scale calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian. The sharp Fermi surface of the non-interacting limit is significantly broadened by the electronic correlations, but retains signatures of the approach to the edges of the first Brillouin zone as the density increases. Finite size scaling of simulations on large lattices allows us to extract the interaction dependence of the antiferromagnetic order parameter, exhibiting its evolution from weak-coupling to the strong-coupling Heisenberg limit. Our lattices provide improved resolution of the momentum distribution, allowing a more quantitative comparison with time-of-flight optical lattice experiments.