Accurate Calculation of Equilibrium Reduced Density Matrix for the System-Bath Model: a Multilayer Multiconfiguration Time-Dependent Hartree Approach and its Comparison to a Multi-Electronic-State Path Integral Molecular Dynamics Approach^†

An efficient and accurate method for computing the equilibrium reduced density matrix is presented for treating open quantum systems characterized by the system-bath model. The method employs the multilayer multiconfiguration time-dependent Hartree theory for imaginary time propagation and an importance sampling procedure for calculating the quantum mechanical trace. The method is applied to the spin-boson Hamiltonian, which leads to accurate results in agreement with those produced by the multi-electronic-state path integral molecular dynamics method.