M ay 1 99 6 A new approach to significantly reduce the negative sign problem in quantum Monte

We present a new approach for Monte Carlo simulations of quantum spin systems which is able to strongly reduce the negative sign problem. Its efficiency is tested on a simple 2-dimensional fermionic model for which we show that our algorithm eliminates the sign problem. The investigation of quantum spin systems is important for understanding the physics related to strongly correlated electrons and high temperature superconductivity. A poverful technique to numerically study quantum spin systems is the quantum Monte Carlo (QMC) method based on the Suzuki-Trotter formula [1]. Unfortunately, QMC can suffer from the negative sign problem (NSP), which becomes exponentially serious on large lattices and at low temperature. In this work we present a new algorithm which is able to strongly reduce this problem. A more detailed description of this algorithm and a rigorous proof of its correctness will be published elsewhere [2]. This algorithm is general and can be applied to any quantum spin system. We have tested its efficiency with a simple 2-dimensional fermionic model and we show that for this model the NSP disappears. We consider a quantum spin system defined on a d-dimensional finite lattice. Its direct simulation is not possible because the requirement in storage and work is exponential in the lattice size of the system. To avoid this complexity, usually one transforms it to a d+1dimensional classical spin system realized by the application of the Suzuki-Trotter formula to the original d-dimensional system. The extra dimension is a discretization of the inverse temperature. We call it time. This classical spin system allows us to use a Monte Carlo approach for evaluating observables. The con figurations v defined on the d+1-dimensional lattice are weighted by w(v) in the partition function Z = ∑