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Variational Monte-Carlo investigation of SU() Heisenberg chains
Motivated by recent experimental progress in the context of ultra-cold
multi-color fermionic atoms in optical lattices, we have investigated the
properties of the SU() Heisenberg chain with totally antisymmetric
irreducible representations, the effective model of Mott phases with
particles per site. These models have been studied for arbitrary and
with non-abelian bosonization [I. Affleck, Nuclear Physics B 265, 409 (1986);
305, 582 (1988)], leading to predictions about the nature of the ground state
(gapped or critical) in most but not all cases. Using exact diagonalization and
variational Monte-Carlo based on Gutzwiller projected fermionic wave functions,
we have been able to verify these predictions for a representative number of
cases with and , and we have shown that the opening of
a gap is associated to a spontaneous dimerization or trimerization depending on
the value of m and N. We have also investigated the marginal cases where
abelian bosonization did not lead to any prediction. In these cases,
variational Monte-Carlo predicts that the ground state is critical with
exponents consistent with conformal field theory.Comment: 9 pages, 10 figures, 3 table
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