Msldc. De Jongh et al., Incorporation of density-matrix wave functions in Monte Carlo simulations:Application to the frustrated Heisenberg model, PHYS REV B, 62(22), 2000, pp. 14844-14854
We combine the density-matrix renormalization-group (DMRG) technique with G
reen function Monte Carlo (GFMC) simulations using a special representation
of the DMRG wave function. As a test case we apply the method to the two-d
imensional frustrated Heisenberg antiferromagnet. By supplementing the bran
ching in GFMC simulations with stochastic reconfiguration we get a stable s
imulation with a small variance also in the region when the fluctuations du
e to the minus sign problem are maximal. The sensitivity of the results to
the choice of the guiding wave function is extensively investigated. In agr
eement with earlier calculations it is found from the DMRG wave function th
at for small ratios of the next-nearest-to-nearest neighbor coupling streng
th the system orders as a Neel-type antiferromagnet and for large ratios as
a columnar antiferromagnet. The spin stiffness suggests an intermediate re
gime without magnetic long-range order. The energy curve indicates that the
columnar phase is separated from the intermediate phase by a first-order t
ransition. The combination of the DMRG and GFMC techniques allows us to sub
stantiate this picture by calculating also the spin correlations in the sys
tem. We observe a pattern of spin correlations in the intermediate regime w
hich is in between dimerlike and plaquette-type ordering, states that have
recently been suggested. It is a state with strong dimerization in one dire
ction and weaker dimerization in the perpendicular direction and thus it la
cks the square symmetry of the plaquette state.