33 research outputs found
Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: Slater vs Mott-Heisenberg
We study antiferromagnetism and single-particle properties in the
two-dimensional half-filled Hubbard model at low temperature. Collective spin
fluctuations are governed by a non-linear sigma model that we derive from the
Hubbard model for any value of the Coulomb repulsion. As the Coulomb repulsion
increases, the ground state progressively evolves from a Slater to a
Mott-Heisenberg antiferromagnet. At finite temperature, we find a
metal-insulator transition between a pseudogap phase at weak coupling and a
Mott-Hubbard insulator at strong coupling.Comment: Revised version, to appear in EuroPhys. Letters (epl style included
Anomalous Spin Dynamics of Hubbard Model on Honeycomb Lattices
In this paper, the honeycomb Hubbard model in optical lattices is
investigated using O(3) non-linear sigma model. A possible quantum non-magnetic
insulator in a narrow parameter region is found near the metal-insulator
transition. We study the corresponding dynamics of magnetic properties, and
find that the narrow region could be widened by hole doping.Comment: 9 pages, 12 figure
Quantum Non-Magnetic state near Metal-Insulator Transition - a Possible Candidate of Spin Liquid State
In this paper, based on the formulation of an O(3) non-linear sigma model, we
study the two-dimensional Pi-flux Hubbard model at half-filling. A quantum
non-magnetic insulator is explored near the metal-insulator transition that may
be a possible candidate of the spin liquid state. Such quantum non-magnetic
insulator on square lattice is not induced by frustrations. Instead, it
originates from quantum spin fluctuations with relatively small effective spin
moments. In the strong-coupling limit, our results of the spin velocity and
spin order parameter agree with results obtained from earlier calculations.Comment: 6 pages, 6 figures, Version of publication in EPL, removing the
contents of honeycomb lattice and adding some contents of square lattic
Neel Order and Electron Spectral Functions in the Two-Dimensional Hubbard Model: a Spin-Charge Rotating Frame Approach
Using recently developed quantum SU(2)xU(1) rotor approach, that provides a
self-consistent treatment of the antiferromagnetic state we have performed
electronic spectral function calculations for the Hubbard model on the square
lattice. The collective variables for charge and spin are isolated in the form
of the space-time fluctuating U(1) phase field and rotating spin quantization
axis governed by the SU(2) symmetry, respectively. As a result interacting
electrons appear as composite objects consisting of bare fermions with attached
U(1) and SU(2) gauge fields. This allows us to write the fermion Green's
function in the space-time domain as the product CP^1 propagator resulting from
the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion
correlation function. As a result the problem of calculating the spectral line
shapes now becomes one of performing the convolution of spin, charge and
pseudo-fermion Green's functions. The collective spin and charge fluctuations
are governed by the effective actions that are derived from the Hubbard model
for any value of the Coulomb interaction. The emergence of a sharp peak in the
electron spectral function in the antiferromagnetic state indicates the decay
of the electron into separate spin and charge carrying particle excitations.Comment: 16 pages, 5 figures, submitted to Phys. Rev.
Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: a non-linear sigma model approach
We describe a low-temperature approach to the two-dimensional half-filled
Hubbard model which allows us to study both antiferromagnetism and
single-particle properties. This approach ignores amplitude fluctuations of the
antiferromagnetic (AF) order parameter and is valid below a crossover
temperature which marks the onset of AF short-range order. Directional
fluctuations (spin waves) are described by a non-linear sigma model
(NLM) that we derive from the Hubbard model. At zero temperature and
weak coupling, our results are typical of a Slater antiferromagnet. The AF gap
is exponentially small; there are well-defined Bogoliubov quasi-particles
(QP's) (carrying most of the spectral weight) coexisting with a high-energy
incoherent excitation background. As increases, the Slater antiferromagnet
progressively becomes a Mott-Heisenberg antiferromagnet. The Bogoliubov bands
evolve into Mott-Hubbard bands separated by a large AF gap. A significant
fraction of spectral weight is transferred from the Bogoliubov QP's to
incoherent excitations. At finite temperature, there is a metal-insulator
transition between a pseudogap phase at weak coupling and a Mott-Hubbard
insulator at strong coupling. Finally, we point out that our results
straightforwardly translate to the half-filled attractive Hubbard model, where
the charge and pairing fluctuations combine to
form an order parameter with SO(3) symmetry.Comment: Revtex4, 19 pages, 14 figures; (v2) final version as publishe
Two-Particle-Self-Consistent Approach for the Hubbard Model
Even at weak to intermediate coupling, the Hubbard model poses a formidable
challenge. In two dimensions in particular, standard methods such as the Random
Phase Approximation are no longer valid since they predict a finite temperature
antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The
Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as
particle conservation, the Pauli principle, the local moment and local charge
sum rules. The self-energy formula does not assume a Migdal theorem. There is
consistency between one- and two-particle quantities. Internal accuracy checks
allow one to test the limits of validity of TPSC. Here I present a pedagogical
review of TPSC along with a short summary of existing results and two case
studies: a) the opening of a pseudogap in two dimensions when the correlation
length is larger than the thermal de Broglie wavelength, and b) the conditions
for the appearance of d-wave superconductivity in the two-dimensional Hubbard
model.Comment: Chapter in "Theoretical methods for Strongly Correlated Systems",
Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages.
Misprint in Eq.(23) corrected (thanks D. Bergeron