Direct calculation of the Entanglement Spectrum in Quantum Monte Carlo with application to \textit{ab initio} Hamiltonians

Abstract

Several algorithms have been proposed to calculate the spatial entanglement spectrum from high order Renyi entropies. In this work 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 coordinates. We demonstrate the method by applying it to the Hydrogen and Nitrogen molecules and describe for the first time how the spatial entanglement spectrum encodes a covalent bond that includes all the many body correlations.

6 pages, 3 figures

References in corpus (8)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Universal entanglement entropy in 2D conformal quantum critical points
• Entanglement entropy of critical spin liquids
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
• Renyi Entropy of the Interacting Fermi Liquid
• Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model
• Particle entanglement in continuum many-body systems via quantum Monte Carlo

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