Calculating the entanglement spectrum in quantum Monte Carlo with application to ab initio Hamiltonians

摘要

Several algorithms have been proposed to calculate the spatial entanglement spectrum from high order Renyi entropies and maximum entropy techniques. We present an alternative approach for computing the entanglement spectrum with quantum Monte Carlo for both continuum and lattice Hamiltonians. This method provides direct access to the matrix elements of the spatially reduced density matrix and we determine an estimator that can be used in variational Monte Carlo as well as other Monte Carlo methods. The algorithm is based on using a generalization of the swap operator, which can be extended to calculate a general class of density matrices that can include combinations of spin, space, particle, and even momentum degrees of freedom. We demonstrate the method by applying it to the H_2 and N_2 molecules and describe how the spatial entanglement spectrum encodes a covalent bond that includes all the many body correlations.