Incorporation of density-matrix wave functions in Monte Carlo simulations:Application to the frustrated Heisenberg model

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.