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We revisit the connection between von Neumann algebra index and relative entropy. We observe that the Pimsner-Popa index connects to maximal sandwiched p-R\'enyi relative entropy for all p between 1/2 and infinity, including the Umegaki's relative entropy at p=1. Based on that, we introduce a new notation of maximal relative entropy for a inclusion of finite von Neumann algebras. These maximal relative entropy generalizes subfactors index and has application in estimating decoherence time of quantum Markov semigroup
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Quantification of electron correlation for approximate quantum calculations
State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrödinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater–Jastrow wave functions.
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- Award ID(s):
- 1931258
- PAR ID:
- 10440032
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 157
- Issue:
- 19
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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