Implications of pinned occupation numbers for natural orbital expansions: I. Generalizing the concept of active spaces

Abstract

The concept of active spaces simplifies the description of interacting quantum many-body systems by restricting to a neighborhood of active orbitals around the Fermi level. The respective wavefunction ansatzes which involve all possible electron configurations of active orbitals can be characterized by the saturation of a certain number of Pauli constraints   n 0 1 i , identifying the occupied core orbitals (n i =1) and the inactive virtual orbitals (n j =0). In Part I, we generalize this crucial concept of active spaces by referring to the generalized Pauli constraints. To be more specific, we explain and illustrate that the saturation of any such constraint on fermionic occupation numbers characterizes a distinctive set of active electron configurations. A converse form of this selection rule establishes the basis for corresponding multiconfigurational wavefunction ansatzes. In Part II, we provide rigorous derivations of those findings. Moroever, we extend our results to non-fermionic multipartite quantum systems, revealing that extremal single-body information has always strong implications for the multipartite quantum state. In that sense, our work also confirms that pinned quantum systems define new physical entities and the presence of pinnings reflect the existence of (possibly hidden) ground state symmetries.

A complete hierarchy for the pure state marginal problem in quantum mechanics

“…(52) and (53) and the fact that the set of separable states is closed imply that Φ AB satisfies all constraints in Eqs. (14), (15), and (16). Then, Theorem 2 follows directly from Theorem 1.…”

“…This is relevant in condensed matter physics, where one may ask whether a state is the unique ground state of a local Hamiltonian 8 , 9 . Many other cases, such as marginal problems for Gaussian and symmetric states 10 , 11 and applications in quantum correlation 12 , quantum causality 13 , and interacting quantum many-body systems 14 , 15 have been studied.…”

From Fredholm to Schrödinger via Eikonal: A New Formalism for Revealing Unknown Properties of Natural Orbitals

“…For example, their occupation numbers enter the generalized Pauli constraints, fulfillment of which is essential for proper formulation of the density matrix functional theory (DMFT) that commonly relies on a convenient (though far from optimal) parameterization in terms of the NOs . Both the NOs and their occupation numbers appear in diverse facets of quantum chemistry such as systematic construction of accurate basis sets, formal and practical definitions of active spaces in multiconfiguration self-consistent-field (MC SCF) and complete active space (CAS) SCF calculations, time propagation of orbitals in time-dependent density functional theory (TD DFT) calculations, highly accurate prediction of electronic spectra of atoms, and computationally efficient implementations of Monte Carlo CI and correlated calculations employing plane waves as basis functions, to name a few.…”

Experimental proposal to probe the extended Pauli principle

“…This is where the extended Pauli principle adds real constraints to the system, that are overlooked (not imposed) by the regular Pauli principle. This situation has recently been investigated in a variety of systems both analytically and numerically [4][5][6][12][13][14][15][16]. It was also simulated on the IBM Quantum Experience, where the fermionic system was mapped to qubits [17].…”