Classifying fermionic states via many-body correlation measures

Quantum, vol. 9, pp. 1705

Abstract

Understanding the structure of quantum correlations in a many-body system is key to its computational treatment. For fermionic systems, correlations can be defined as deviations from Slater determinant states. The link between fermionic correlations and efficient computational physics methods is actively studied but remains ambiguous. We make progress in establishing this connection mathematically. In particular, we find a rigorous classification of states relative to k -fermion correlations, which admits a computational physics interpretation. Correlations are captured by a measure ωk , a function of k -fermion reduced density matrix that we call twisted purity. A condition ωk=0 for a given k puts the state in a class Gk of correlated states. Sets Gk are nested in k , and Slater determinants correspond to k=1 . Classes Gk=O(1) are shown to be physically relevant, as ωk vanishes or nearly vanishes for truncated configuration-interaction states, perturbation series around Slater determinants, and some nonperturbative eigenstates of the 1D Hubbard model. For each k=O(1) , we give an explicit ansatz with a polynomial number of parameters that covers all states in Gk . Potential applications of this ansatz and its connections to the coupled-cluster wavefunction are discussed.

Authors 3

1. Mykola Semenyakin Aachen Instituut-Lorentz

   Leiden University · Perimeter Institute

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

   Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada

2. Yevheniia Cheipesh Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

3. Yaroslav Herasymenko

   QuTech · Delft University of Technology · Centrum Wiskunde & Informatica · QuSoft

   Affiliation as printed

   Delft Institute of Applied Mathematics, TU Delft, 2628 CD Delft, The Netherlands

   QuSoft and CWI, Science Park 123, 1098 XG Amsterdam, The Netherlands

   QuTech, TU Delft, P.O. Box 5046, 2600 GA Delft, The Netherlands