Abstract
This paper discusses a classical simulation to compute the partition function (or free energy) of generic one-dimensional quantum many-body systems. Many numerical methods have previously been developed to approximately solve one-dimensional quantum systems. However, there exists no exact proof that arbitrary one-dimensional quantum Gibbs states can be efficiently solved by a classical computer. Therefore, the aim of this paper is to prove this with the clustering properties for arbitrary finite temperatures β⁻¹. We explicitly show an efficient algorithm that approximates the partition function up to an error ε with a computational cost that scales as n· poly(1/ε), where the degree of the polynomial depends on β as e^O(β). Extending the analysis to higher dimensions at high temperatures, we obtain a weaker result for the computational cost n\cdot (1/\epsilon)^{\log^{D-1} (1/\epsilon)}, where D is the lattice dimension.