Figure 3
(Color online) Total energy per site differences
, separated into kinetic energy
, electrostatic energy
, and exchange energy
contributions as a function of magnetic length
in lattice constant
units. The total-energy differences were fitted to a
curve. The fitting parameters are listed in Table . Left panel: Energy differences between F and SDW solutions
. These results were obtained with interaction parameter values
and
for which SDW is the lowest energy configuration. The more negative values of exchange energy in the SDW state compensates the kinetic-energy penalty related to the inhomogeneous accumulation of the electron wave functions at alternating lattice sites. The electrostatic energy differences are zero thanks to the uniform electron density for both solutions. Right panel: Same as the previous figure but for
. The interaction parameters in this case are
and
for which CDW is the lowest-energy configuration. When the on-site repulsion
is small enough that the electrostatic energy penalty for the inhomogeneous charge distribution is small, exchange is the main contribution driving the CDW instability. However, in the case illustrated here
is so small that the electrostatic part of the Hamiltonian does play an important role in favoring the CDW state. The energy contributions follow a magnetic-field decay law that deviates more from
than in the previous case because the on-site interaction
plays an essential role.
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