Quantum Monte Carlo Calculations of Entanglement

Lei Wang, Matthias Troyer

We present a new algorithm for calculating the Renyi entanglement entropy of interacting fermions using the continuous-time quantum Monte Carlo method. The algorithm only samples the interaction correction of the entanglement entropy, which by design ensures the efficient calculation of weakly interacting systems. Combined with Monte Carlo reweighting, the algorithm also performs well for systems with strong interactions. We demonstrate the potential of this method by studying the quantum entanglement signatures of the charge-density-wave transition of interacting fermions on a square lattice.

Tommaso Roscilde, Paola Verrucchi, Andrea Fubini +2 more

Norm M. Tubman, David ChangMo Yang

Several algorithms have been proposed to calculate the spatial entanglement spectrum from high order R\'enyi 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 ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$ molecules and describe how the spatial entanglement spectrum encodes a covalent bond that includes all the many body correlations.

Roger G. Melko

Ryo Maezono, Hirofumi Watanabe, Shigenori Tanaka +2 more

The total energy of a small polypeptide system is calculated by combining the quantum Monte Carlo (QMC) and fragment molecular orbital (FMO) methods. Electronic correlation is taken into account using Slater–Jastrow wave functions and the variational quantum Monte Carlo (VMC) method. We calculate the energy of the whole system directly and by using the FMO method, finding that the combined QMC–FMO approach works very well.

Manuel Erhard, Mario Krenn, Anton Zeilinger