1 7 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 lattice quantum spin systems which is able to eliminate the negative sign problem. Its complexity is linear in the volume of the lattice. Its efficiency is tested on a simple 2-dimensional fermionic model. 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 (for a review see [1]) based on the Suzuki-Trotter formula [2]. 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 [3]. This algorithm is general and can be applied to any quantum spin system. Its complexity is only linear in the volume of the lattice. 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 co nfigurations v defined on the d+1-dimensional lattice are weighted by w(v) in the partition function Z = ∑ v w(v) (1) The evaluation of the weight w(v) is of small complexity, contrary to the original ddimensional quantum spin system. The price to pay is that the new classical system has a [email protected] 1 partition function for which generally not all weights are positive semidefinite. This fundamental difficulty is usually referred to as the ”negative sign” problem. It is not related to any approxim ations in the Monte Carlo scheme but it describes the fact that the statistical error of the observables can become very large, increasing exponentially in the inverse temperature β and lattice volume. Any classical observable A is measured at the first time slice of the d+1-dimensional lattice by averaging over the sample of configurations generated by the Monte Carlo process. For simplicity, we restrict the discussion to classical observables. The ex pectation value of them can be written < A >w= ∑ v A(v) |w(v)| · sgn(w(v))