188 research outputs found
Ground-state phase diagram of a half-filled one-dimensional extended Hubbard model
The density-matrix renormalization group is used to study the phase diagram
of the one-dimensional half-filled Hubbard model with on-site (U) and
nearest-neighbor (V) repulsion, and hopping t. A critical line V_c(U)
approximately equal to U/2 separates a Mott insulating phase from a
charge-density-wave phase. The formation of bound charge excitations for V > 2t
changes the phase transition from continuous to first order at a tricritical
point U_t = 3.7t, V_t=2t. A frustrating effective antiferromagnetic spin
coupling induces a bond-order-wave phase on the critical line V_c(U) for U_t <
U < 7-8 t.Comment: 4 pages (REVTEX 4), 3 EPS figures, shorter abstract, text and
references modifie
Perturbation theory for optical excitations in the one-dimensional extended Peierls--Hubbard model
For the one-dimensional, extended Peierls--Hubbard model we calculate
analytically the ground-state energy and the single-particle gap to second
order in the Coulomb interaction for a given lattice dimerization. The
comparison with numerically exact data from the Density-Matrix Renormalization
Group shows that the ground-state energy is quantitatively reliable for Coulomb
parameters as large as the band width. The single-particle gap can almost
triple from its bare Peierls value before substantial deviations appear. For
the calculation of the dominant optical excitations, we follow two approaches.
In Wannier theory, we perturb the Wannier exciton states to second order. In
two-step perturbation theory, similar in spirit to the GW-BSE approach, we form
excitons from dressed electron-hole excitations. We find the Wannier approach
to be superior to the two-step perturbation theory. For singlet excitons,
Wannier theory is applicable up to Coulomb parameters as large as half band
width. For triplet excitons, second-order perturbation theory quickly fails
completely.Comment: 32 pages, 12 figures, submtted to JSTA
Charge and spin order in one-dimensional electron systems with long-range Coulomb interactions
We study a system of electrons interacting through long--range Coulomb forces
on a one--dimensional lattice, by means of a variational ansatz which is the
strong--coupling counterpart of the Gutzwiller wave function. Our aim is to
describe the quantum analogue of Hubbard's classical ``generalized Wigner
crystal''. We first analyse charge ordering in a system of spinless fermions,
with particular attention to the effects of lattice commensurability. We argue
that for a general (rational) number of electrons per site there are three
regimes, depending on the relative strength of the long--range Coulomb
interaction (as compared to the hopping amplitude ). For very large the
quantum ground state differs little from Hubbard's classical solution, for
intermediate to large values of we recover essentially the Wigner crystal
of the continuum model, and for small the charge modulation amounts to a
small--amplitude charge--density wave. We then include the spin degrees of
freedom and show that in the Wigner crystal regimes (i.e. for large ) they
are coupled by an antiferromagnetic kinetic exchange , which turns out to be
smaller than the energy scale governing the charge degrees of freedom. Our
results shed new light on the insulating phases of organic quasi--1D compounds
where the long--range part of the interaction is unscreened, and magnetic and
charge orderings coexist at low temperatures.Comment: 11 pages, 7 figures, accepted for publication on Phys. Rev.
Optical excitations of Peierls-Mott insulators with bond disorder
The density-matrix renormalization group (DMRG) is employed to calculate
optical properties of the half-filled Hubbard model with nearest-neighbor
interactions. In order to model the optical excitations of oligoenes, a Peierls
dimerization is included whose strength for the single bonds may fluctuate.
Systems with up to 100 electrons are investigated, their wave functions are
analyzed, and relevant length-scales for the low-lying optical excitations are
identified. The presented approach provides a concise picture for the size
dependence of the optical absorption in oligoenes.Comment: 12 pages, 13 figures, submitted to Phys. Rev.
Quantum global vortex strings in a background field
We consider quantum global vortex string correlation functions, within the
Kalb-Ramond framework, in the presence of a background field-strength tensor
and investigate the conditions under which this yields a nontrivial
contribution to those correlation functions. We show that a background field
must be supplemented to the Kalb-Ramond theory, in order to correctly describe
the quantum properties of the vortex strings. The explicit form of this
background field and the associated quantum vortex string correlation function
are derived. The complete expression for the quantum vortex creation operator
is explicitly obtained. We discuss the potential applicability of our results
in the physics of superfluids and rotating Bose-Einstein condensates.Comment: To appear in Journal of Physics A: Mathematical and Genera
Charge density wave and quantum fluctuations in a molecular crystal
We consider an electron-phonon system in two and three dimensions on square,
hexagonal and cubic lattices. The model is a modification of the standard
Holstein model where the optical branch is appropriately curved in order to
have a reflection positive Hamiltonian. Using infrared bounds together with a
recent result on the coexistence of long-range order for electron and phonon
fields, we prove that, at sufficiently low temperatures and sufficiently strong
electron-phonon coupling, there is a Peierls instability towards a period two
charge-density wave at half-filling. Our results take into account the quantum
fluctuations of the elastic field in a rigorous way and are therefore
independent of any adiabatic approximation. The strong coupling and low
temperature regime found here is independent of the strength of the quantum
fluctuations of the elastic field.Comment: 15 pages, 1 figur
Comparison of Variational Approaches for the Exactly Solvable 1/r-Hubbard Chain
We study Hartree-Fock, Gutzwiller, Baeriswyl, and combined
Gutzwiller-Baeriswyl wave functions for the exactly solvable one-dimensional
-Hubbard model. We find that none of these variational wave functions is
able to correctly reproduce the physics of the metal-to-insulator transition
which occurs in the model for half-filled bands when the interaction strength
equals the bandwidth. The many-particle problem to calculate the variational
ground state energy for the Baeriswyl and combined Gutzwiller-Baeriswyl wave
function is exactly solved for the~-Hubbard model. The latter wave
function becomes exact both for small and large interaction strength, but it
incorrectly predicts the metal-to-insulator transition to happen at infinitely
strong interactions. We conclude that neither Hartree-Fock nor Jastrow-type
wave functions yield reliable predictions on zero temperature phase transitions
in low-dimensional, i.e., charge-spin separated systems.Comment: 23 pages + 3 figures available on request; LaTeX under REVTeX 3.
Nonlinear Optical Response of Spin Density Wave Insulators
We calculate the third order nonlinear optical response in the Hubbard model
within the spin density wave (SDW) mean field ansatz in which the gap is due to
onsite Coulomb repulsion. We obtain closed-form analytical results in one
dimension (1D) and two dimension (2D), which show that nonlinear optical
response in SDW insulators in 2D is stronger than both 3D and 1D. We also
calculate the two photon absorption (TPA) arising from the stress tensor term.
We show that in the SDW, the contribution from stress tensor term to the
low-energy peak corresponding to two photon absorption becomes identically zero
if we consider the gauge invariant current properly.Comment: we use \psfrag in figur
The effects of the next-nearest-neighbour density-density interaction in the atomic limit of the extended Hubbard model
We have studied the extended Hubbard model in the atomic limit. The
Hamiltonian analyzed consists of the effective on-site interaction U and the
intersite density-density interactions Wij (both: nearest-neighbour and
next-nearest-neighbour). The model can be considered as a simple effective
model of charge ordered insulators. The phase diagrams and thermodynamic
properties of this system have been determined within the variational approach,
which treats the on-site interaction term exactly and the intersite
interactions within the mean-field approximation. Our investigation of the
general case taking into account for the first time the effects of
longer-ranged density-density interaction (repulsive and attractive) as well as
possible phase separations shows that, depending on the values of the
interaction parameters and the electron concentration, the system can exhibit
not only several homogeneous charge ordered (CO) phases, but also various phase
separated states (CO-CO and CO-nonordered). One finds that the model considered
exhibits very interesting multicritical behaviours and features, including
among others bicritical, tricritical, critical-end and isolated critical
points.Comment: 12 pages, 7 figures; final version, pdf-ReVTeX; corrected typos in
reference; submitted to Journal of Physics: Condensed Matte
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