435 research outputs found
The Gutzwiller wave function as a disentanglement prescription
The Gutzwiller variational wave function is shown to correspond to a
particular disentanglement of the thermal evolution operator, and to be
physically consistent only in the temperature range U<<kT<<E_F, the Fermi
energy of the non-interacting system. The correspondence is established without
using the Gutzwiller approximation. It provides a systematic procedure for
extending the ansatz to the strong-coupling regime. This is carried out to
infinite order in a dominant class of commutators. The calculation shows that
the classical idea of suppressing double occupation is replaced at low
temperatures by a quantum RVB-like condition, which involves phases at
neighboring sites. Low-energy phenomenologies are discussed in the light of
this result.Comment: Final version as accepted in EPJ B, 10 pages, no figure
Exact density matrix of the Gutzwiller wave function: II. Minority spin component
The density matrix, i.e. the Fourier transform of the momentum distribution,
is obtained analytically for all magnetization of the Gutzwiller wave function
in one dimension with exclusion of double occupancy per site. The present
result complements the previous analytic derivation of the density matrix for
the majority spin. The derivation makes use of a determinantal form of the
squared wave function, and multiple integrals over particle coordinates are
performed with the help of a diagrammatic representation. In the thermodynamic
limit, the density matrix at distance x is completely characterized by
quantities v_c x and v_s x, where v_s and v_c are spin and charge velocities in
the supersymmetric t-J model for which the Gutzwiller wave function gives the
exact ground state. The present result then gives the exact density matrix of
the t-J model for all densities and all magnetization at zero temperature.
Discontinuity, slope, and curvature singularities in the momentum distribution
are identified. The momentum distribution obtained by numerical Fourier
transform is in excellent agreement with existing result.Comment: 20 pages, 10 figure
Exact analytic results for the Gutzwiller wave function with finite magnetization
We present analytic results for ground-state properties of Hubbard-type
models in terms of the Gutzwiller variational wave function with non-zero
values of the magnetization m. In dimension D=1 approximation-free evaluations
are made possible by appropriate canonical transformations and an analysis of
Umklapp processes. We calculate the double occupation and the momentum
distribution, as well as its discontinuity at the Fermi surface, for arbitrary
values of the interaction parameter g, density n, and magnetization m. These
quantities determine the expectation value of the one-dimensional Hubbard
Hamiltonian for any symmetric, monotonically increasing dispersion epsilon_k.
In particular for nearest-neighbor hopping and densities away from half filling
the Gutzwiller wave function is found to predict ferromagnetic behavior for
sufficiently large interaction U.Comment: REVTeX 4, 32 pages, 8 figure
On the evaluation of matrix elements in partially projected wave functions
We generalize the Gutzwiller approximation scheme to the calculation of
nontrivial matrix elements between the ground state and excited states. In our
scheme, the normalization of the Gutzwiller wave function relative to a
partially projected wave function with a single non projected site (the
reservoir site) plays a key role. For the Gutzwiller projected Fermi sea, we
evaluate the relative normalization both analytically and by variational
Monte-Carlo (VMC). We also report VMC results for projected superconducting
states that show novel oscillations in the hole density near the reservoir
site
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.
Correlated hopping of electrons: Effect on the Brinkman-Rice transition and the stability of metallic ferromagnetism
We study the Hubbard model with bond-charge interaction (`correlated
hopping') in terms of the Gutzwiller wave function. We show how to express the
Gutzwiller expectation value of the bond-charge interaction in terms of the
correlated momentum-space occupation. This relation is valid in all spatial
dimensions. We find that in infinite dimensions, where the Gutzwiller
approximation becomes exact, the bond-charge interaction lowers the critical
Hubbard interaction for the Brinkman-Rice metal-insulator transition. The
bond-charge interaction also favors ferromagnetic transitions, especially if
the density of states is not symmetric and has a large spectral weight below
the Fermi energy.Comment: 5 pages, 3 figures; minor changes, published versio
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