41 research outputs found
Ab-Initio Calculation of the Metal-Insulator Transition in Sodium rings and chains and in mixed Sodium-Lithium systems
We study how the Mott metal-insulator transition (MIT) is influenced when we
deal with electrons with different angular momenta. For lithium we found an
essential effect when we include -orbitals in the description of the Hilbert
space. We apply quantum-chemical methods to sodium rings and chains in order to
investigate the analogue of a MIT, and how it is influenced by periodic and
open boundaries. By changing the interatomic distance we analyse the character
of the many-body wavefunction and the charge gap. In the second part we mimic a
behaviour found in the ionic Hubbard model, where a transition from a band to a
Mott insulator occurs. For that purpose we perform calculations for mixed
sodium-lithium rings. In addition, we examine the question of bond alternation
for the pure sodium system and the mixed sodium-lithium system, in order to
determine under which conditions a Peierls distortion occurs.Comment: 8 pages, 7 figures, accepted Eur. J. Phys.
Dielectric catastrophe at the Mott transition
We study the Mott transition as a function of interaction strength in the
half-filled Hubbard chain with next-nearest-neighbor hopping t' by calculating
the response to an external electric field using the Density Matrix
Renormalization Group. The electric susceptibility chi diverges when
approaching the critical point from the insulating side. We show that the
correlation length xi characterizing this transition is directly proportional
to fluctuations of the polarization and that chi ~ xi^2. The critical behavior
shows that the transition is infinite-order for all t', whether or not a spin
gap is present, and that hyperscaling holds.Comment: 4 pages, 4 eps figures, REVTe
From band insulator to Mott insulator in one dimension
We derive the phase diagram for the one-dimensional model of a ferroelectric
perovskite recently introduced by Egami, Ishihara and Tachiki [Science, {\bf
261}, 1307 (1993)]. We show that the interplay between covalency, ionicity and
strong correlations results in a spontaneously dimerized phase which separates
the weak-coupling band insulator from the strong-coupling Mott insulator. The
transition from the band insulator to the dimerized phase is identified as an
Ising critical point. The charge gap vanishes at this single point with the
optical conductivity diverging as . The spin
excitations are gapless above the second transition to the Mott insulator
phase.Comment: 4 pages LaTex (RevTex) and 1 postscript figure included by eps
Effect of Electron Correlation on the Bragg Reflection
We study the effect of correlation on the Bragg reflection in the 3D electron
gas, the 1D Luttinger liquid, and the 1D Hubbard model in an alternating
periodic potential at half-filling. In the last system, we suggest a
Luttinger-liquid-type quasi-metallic state in the crossover region from the
band insulator to the Mott insulator. We explain the appearance of this state
in terms of the incompatibility of the Bragg reflection with the concept of
Luttinger liquids.Comment: 4 pages, 3 figure
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
A quantum Monte Carlo study of the one-dimensional ionic Hubbard model
Quantum Monte Carlo methods are used to study a quantum phase transition in a
1D Hubbard model with a staggered ionic potential (D). Using recently
formulated methods, the electronic polarization and localization are determined
directly from the correlated ground state wavefunction and compared to results
of previous work using exact diagonalization and Hartree-Fock. We find that the
model undergoes a thermodynamic transition from a band insulator (BI) to a
broken-symmetry bond ordered (BO) phase as the ratio of U/D is increased. Since
it is known that at D = 0 the usual Hubbard model is a Mott insulator (MI) with
no long-range order, we have searched for a second transition to this state by
(i) increasing U at fixed ionic potential (D) and (ii) decreasing D at fixed U.
We find no transition from the BO to MI state, and we propose that the MI state
in 1D is unstable to bond ordering under the addition of any finite ionic
potential. In real 1D systems the symmetric MI phase is never stable and the
transition is from a symmetric BI phase to a dimerized BO phase, with a
metallic point at the transition
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 = and U =
that separate the BI and MI phases for a given V. A charge-neutral
spin-singlet exciton band develops in the BI phase (U<) and drops below
the band gap when U exceeds a special point Ue. The exciton gap closes at the
first critical point while the charge and spin gaps persist and coincide
between <U< where the system is dimerized. Both the charge and spin
gaps collapse at U = when the transition to the MI phase occurs. In the
MI phase (U>) 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
Minimal charge gap in the ionic Hubbard model
We study the ionic Hubbard model at temperature T=0 within the mean-field
approximation, and show that the charge gap does not close completely at the
ionic-band insulator to antiferromagnetic insulator transition, contrary to
previous expectations. Furthermore, we find an intermediate phase for on-site
repulsions for different lattices, and calculate the phase diagram for
the ionic Hubbard model with alternating U, corresponding to a Cu-O lattice.Comment: 5 pages with 7 figures; minor correction