Phase diagram of the Hubbard chain with two atoms per cell

We obtain the quantum phase diagram of the Hubbard chain with alternating on-site energy at half filling. The model is relevant for the ferroelectric perovskites and organic mixed-stack donor-acceptor crystals. For any values of the parameters, the band insulator is separated from the Mott insulator by a dimer phase. The boundaries are determined accurately by crossing of excited levels with particular discrete symmetries. We show that these crossings coincide with jumps of charge and spin Berry phases with a clear geometrical meaning.Comment: 5 pages including 2 figures To be published in Phys. Rev. B (Rapid Communications

Charge dynamics in the Mott insulating phase of the ionic Hubbard model

We extend to charge and bond operators the transformation that maps the ionic Hubbard model at half filling onto an effective spin Hamiltonian. Using these operators we calculate the amplitude of the charge density wave in different dimensions. In one dimension, the charge-charge correlations at large distance d decay as 1/(d^3 ln^{3/2}d), in spite of the presence of a charge gap, as a consequence of remaining charge-spin coupling. Bond-bond correlations decay as (-1)^d 1/(d ln^{3/2}d) as in the usual Hubbard model.Comment: 4 pages, no figures, submitted to Phys. Rev. B printing errors corrected and some clarifications adde

Fano resonance in electronic transport through a quantum wire with a side-coupled quantum dot: X-boson treatment

The transport through a quantum wire with a side coupled quantum dot is studied. We use the X-boson treatment for the Anderson single impurity model in the limit of $U=\infty$. The conductance presents a minimum for values of T=0 in the crossover from mixed-valence to Kondo regime due to a destructive interference between the ballistic channel associated with the quantum wire and the quantum dot channel. We obtain the experimentally studied Fano behavior of the resonance. The conductance as a function of temperature exhibits a logarithmic and universal behavior, that agrees with recent experimental results.Comment: 6 pages, 10 eps figs., revtex

Interaction between Kondo impurities in a quantum corral

We calculate the spectral densities for two impurities inside an elliptical quantum corral using exact diagonalization in the relevant Hilbert subspace and embedding into the rest of the system. For one impurity, the space and energy dependence of the change in differential conductance $\Delta = dI/dV$ observed in the quantum mirage experiment is reproduced. In presence of another impurity, $\Delta = dI/dV$ is very sensitive to the hybridization between impurity and bulk. The impurities are correlated ferromagnetically between them. A hopping $\gtrsim 0.15$ eV between impurities destroy the Kondo resonance.Comment: 4 pages, 4 figure

Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model

We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach (g-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for U \approx 2V in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line. In the second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential \Delta or bond alternation \delta. Although the alternating site potential \Delta strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation \delta destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with \delta contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of \Delta or \delta changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.Comment: 24 pages, 20 figures, published versio

Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension

In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twisting operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values $z_L$ measure the overlap between the unique ground state and an excited state. Insulators are characterized by $z_{\infty}\neq 0$. We identify $z_L$ with ground-state expectation values of vertex operators in the sine-Gordon model. This allows an accurate detection of quantum phase transitions in the universality classes of the Gaussian model. We apply this theory to the half-filled extended Hubbard model and obtain agreement with the level-crossing approach.Comment: 4 pages, 3 figure

Phase diagram of the extended Hubbard chain with charge-dipole interactions

We consider a modified extended Hubbard model (EHM) which, in addition to the on-site repulsion U and nearest-neighbor repulsion V, includes polarization effects in second-order perturbation theory. The model is equivalent to an EHM with renormalized U plus a next-nearest-neighbor repulsion term. Using a method based on topological quantum numbers (charge and spin Berry phases), we generalize to finite hopping t the quantum phase diagram in one dimension constructed by van den Brink et al. (Phys. Rev. Lett. 75, 4658 (1995)). At hopping t=0 there are two charge density-wave phases, one spin density-wave phase and one intermediate phase with charge and spin ordering, depending on the parameter values. At t \neq 0 the nature of each phase is confirmed by studying correlation functions. However, in addition to the strong-coupling phases, a small region with bond ordering appears. The region occupied by the intermediate phase first increases and then decreases with increasing t, until it finally disappears for t of the order but larger than U. For small t, the topological transitions agree with the results of second order perturbation theory.Comment: 6 pages, 5 figures, two columns latex version. Accepted for publication in Physical Review B. Mistaken reference 16 has been correcte

Transition from band insulator to Mott insulator in one dimension: Critical behavior and phase diagram

We report a systematic study of the transition from a band insulator (BI) to a Mott insulator (MI) in a one-dimensional Hubbard model at half-filling with an on-site Coulomb interaction U and an alternating periodic site potential V. We employ both the zero-temperature density matrix renormalization group (DMRG) method to determine the gap and critical behavior of the system and the finite-temperature transfer matrix renormalization group method to evaluate the thermodynamic properties. We find two critical points at U = $U_c$ and U = $U_s$ that separate the BI and MI phases for a given V. A charge-neutral spin-singlet exciton band develops in the BI phase (U<$U_c$) and drops below the band gap when U exceeds a special point Ue. The exciton gap closes at the first critical point $U_c$ while the charge and spin gaps persist and coincide between $U_c$<U<$U_s$ where the system is dimerized. Both the charge and spin gaps collapse at U = $U_s$ when the transition to the MI phase occurs. In the MI phase (U>$U_s$) the charge gap increases almost linearly with U while the spin gap remains zero. These findings clarify earlier published results on the same model, and offer insights into several important issues regarding an appropriate scaling analysis of DMRG data and a full physical picture of the delicate nature of the phase transitions driven by electron correlation. The present work provides a comprehensive understanding for the critical behavior and phase diagram for the transition from BI to MI in one-dimensional correlated electron systems with a periodic alternating site potential.Comment: long version, 10 figure

From Gapped Excitons to Gapless Triplons in One Dimension

Often, exotic phases appear in the phase diagrams between conventional phases. Their elementary excitations are of particular interest. Here, we consider the example of the ionic Hubbard model in one dimension. This model is a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong interaction. Inbetween, a spontaneously dimerized insulator (SDI) occurs which is governed by energetically low-lying charge and spin degrees of freedom. Applying a systematically controlled version of the continuous unitary transformations (CUTs) we are able to determine the dispersions of the elementary charge and spin excitations and of their most relevant bound states on equal footing. The key idea is to start from an externally dimerized system using the relative weak interdimer coupling as small expansion parameter which finally is set to unity to recover the original model.Comment: 18 pages, 10 figure

Electron transport across a quantum wire in the presence of electron leakage to a substrate

We investigate electron transport through a mono-atomic wire which is tunnel coupled to two electrodes and also to the underlying substrate. The setup is modeled by a tight-binding Hamiltonian and can be realized with a scanning tunnel microscope (STM). The transmission of the wire is obtained from the corresponding Green's function. If the wire is scanned by the contacting STM tip, the conductance as a function of the tip position exhibits oscillations which may change significantly upon increasing the number of wire atoms. Our numerical studies reveal that the conductance depends strongly on whether or not the substrate electrons are localized. As a further ubiquitous feature, we observe the formation of charge oscillations.Comment: 7 pages, 7 figure