We present a systematic investigation of the special twist method introduced by Rajagopal et al. [Phys. Rev. B 51, 10591 (1995)] for reducing finite-size effects in correlated calculations of periodic extended systems with Coulomb interactions and Fermi statistics. We propose a procedure for finding special twist values which, at variance with previous applications of this method, reproduce the energy of the mean-field infinite-size limit solution within an adjustable (arbitrarily small) numerical error. This choice of the special twist is shown to be the most accurate single-twist solution for curing one-body finite-size effects in correlated calculations. For these reasons we dubbed our procedure ``exact special twist'' (EST). EST only needs a fully converged independent-particles or mean-field calculation within the primitive cell and a simple fit to find the special twist along a specific direction in the Brillouin zone. We first assess the performances of EST in a simple correlated model such as the three-dimensional electron gas. Afterwards, we test its efficiency within ab initio quantum Monte Carlo simulations of metallic elements of increasing complexity. We show that EST displays an overall good performance in reducing finite-size errors comparable to the widely used twist average technique but at a much lower computational cost since it involves the evaluation of just one wave function. We also demonstrate that the EST method shows similar performances in the calculation of correlation functions, such as the ionic forces for structural relaxation and the pair radial distribution function in liquid hydrogen. Our conclusions point to the usefulness of EST for correlated supercell calculations; our method will be particularly relevant when the physical problem under consideration requires large periodic cells.
Special unextendible entangled basis of "type
k" (SUEBk), a set of incomplete orthonormal special entangled states of "type
k" whose complementary space has no special entangled state of "type
k". This concept can be seem as a generalization of the unextendible product basis (UPB) introduced by Bennett et al. in [ Phys. Rev. Lett. \textbf{82}, 5385(1999) ] and the unextendible maximally entangled basis (UMEB) introduced by Bravyi and Smolin in [Phys. Rev. A \textbf{84}, 042306(2011)]. We present an efficient method to construct sets of SUEBk. The main strategy here is to decompose the whole space into two subspaces such that the rank of one subspace can be easily upper bounded by
k while the other one can be generated by two kinds of the special entangled states of type
k. This method is very effective for those
k=pm≥3 where
p is a prime number. For these cases, we can otain sets of SUEBk with continuous integer cardinality when the local dimensions are large. Moreover, one can find that our method here can be easily extended when there are more than two kinds of the special entangled states of type
k at hand.