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

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Abstract
We combine the density-matrix renormalization-group (DMRG) technique with Green 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-dimensional frustrated Heisenberg antiferromagnet. By supplementing the branching in GFMC simulations with stochastic reconfiguration we get a stable simulation with a small variance also in the region where the fluctuations due to the minus sign problem are maximal. The sensitivity of the results to the choice of the guiding wave function is extensively investigated. In agreement with earlier calculations it is found from the DMRG wave function that for small ratios of the next-nearest-to-nearest neighbor coupling strength the system orders as a Néel-type antiferromagnet and for large ratios as a columnar antiferromagnet. The spin stiffness suggests an intermediate regime without magnetic long-range order. The energy curve indicates that the columnar phase is separated from the intermediate phase by a first-order transition. The combination of the DMRG and GFMC techniques allows us to substantiate this picture by calculating also the spin correlations in the system. We observe a pattern of spin correlations in the intermediate regime which is in between dimerlike and plaquette-type ordering, states that have recently been suggested. It is a state with strong dimerization in one direction and weaker dimerization in the perpendicular direction and thus it lacks the square symmetry of the plaquette state.