Structure of the one‐electron reduced density matrix from the generalized <scp>P</scp>auli exclusion principle

Chakraborty, Romit; Mazziotti, David A.

doi:10.1002/qua.24934

Cited by 22 publications

(22 citation statements)

References 51 publications

(120 reference statements)

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“…Only recently has the problem in the simplest case of m = 1 been solved [10], generalizing the equalities and inequalities in (1) systematically. This has led to a burst of studies of the relevance and implications of the so-called generalized Pauli constraints like (1) in atoms, molecules, and model systems [11][12][13][14][15][16][17][18][19][20]. As for the next case of m = 2 (which is possibly of more interest from the point of view of calculating the * wdlang06@163.com † mauser@courant.nyu.edu ground state energy of a multi-electron system), a systematic procedure for generating the N -representability conditions on the two-particle reduced density matrix has been derived by Mazziotti [21].…”

Section: Introductionmentioning

confidence: 99%

Optimal Slater-determinant approximation of fermionic wave functions

Zhang

Mauser

2016

Phys. Rev. A

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We study the optimal Slater-determinant approximation of an N -fermion wave function analytically. That is, we seek the Slater-determinant (constructed out of N orthonormal single-particle orbitals) wave function having largest overlap with a given N -fermion wave function. Some simple lemmas have been established and their usefulness is demonstrated on some structured states, such as the Greenberger-Horne-Zeilinger state. In the simplest nontrivial case of three fermions in six orbitals, which the celebrated Borland-Dennis discovery is about, the optimal Slater approximation wave function is proven to be built out of the natural orbitals in an interesting way. We also show that the Hadamard inequality is useful for finding the optimal Slater approximation of some special target wave functions.

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Section: Introductionmentioning

confidence: 99%

Optimal Slater-determinant approximation of fermionic wave functions

Zhang

Mauser

2016

Phys. Rev. A

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“…Due to its striking consequences, a central question is whether exact pinning actually occurs in realistic fermionic quantum systems. While analytic results for a harmonic model system suggest a negative answer arXiv:1710.03074v2 [quant-ph] 17 May 2018 [8,22,24], various studies of small atoms and molecules [7,11,16,17,19,23] seem to confirm the occurrence of pinning in ground states, and hence emphasize the relevance of the GPCs in quantum chemistry. However, these numerical studies may be inconclusive for two reasons: First, they are based on very small active spaces of only 6 to 10 spin-orbitals and might therefore fail to accurately capture the true physical situation.…”

Section: Introductionmentioning

confidence: 99%

Generalized Pauli constraints in small atoms

et al. 2018

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The natural occupation numbers of fermionic systems are subject to non-trivial constraints, which include and extend the original Pauli principle. A recent mathematical breakthrough has clarified their mathematical structure and has opened up the possibility of a systematic analysis. Early investigations have found evidence that these constraints are exactly saturated in several physically relevant systems; e.g. in a certain electronic state of the Beryllium atom. It has been suggested that in such cases, the constraints, rather than the details of the Hamiltonian, dictate the system's qualitative behavior. Here, we revisit this question with state-of-the-art numerical methods for small atoms. We find that the constraints are, in fact, not exactly saturated, but that they lie much closer to the surface defined by the constraints than the geometry of the problem would suggest. While the results seem incompatible with the statement that the generalized Pauli constraints drive the behavior of these systems, they suggest that the qualitatively correct wave-function expansions can in some systems already be obtained on the basis of a limited number of Slater determinants, which is in line with numerical evidence from quantum chemistry.

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“…A pure N ‐electron quantum system is representable by a single N ‐electron quantum‐mechanical wave function. Recently, the generalized Pauli constraints have been systematically derived for arbitrary numbers of electrons and orbitals and applied to closed, time‐independent systems such as atoms and molecules as well exciton dynamics in photosynthetic light harvesting …”

Section: Introductionmentioning

confidence: 99%

“…[5,6] A pure N-electron quantum system is representable by a single N-electron quantum-mechanical wave function. Recently, the generalized Pauli constraints have been systematically derived for arbitrary numbers of electrons and orbitals [7,8] and applied to closed, time-independent systems such as atoms and molecules [9][10][11][12][13][14][15][16] as well exciton dynamics in photosynthetic light harvesting. [17] When the natural occupation numbers are ordered from largest to smallest, the inequalities of the generalized Pauli constraints define a convex set (polytope).…”

Section: Introductionmentioning

confidence: 99%

Role of the generalized pauli constraints in the quantum chemistry of excited states

Chakraborty

Mazziotti

2016

Int J of Quantum Chemistry

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The Pauli exclusion principle requires that spin orbitals have occupations between zero and one. For pure quantum systems, however, the occupations of the spin orbitals are constrained by additional inequalities known as the generalized Pauli constraints. If the occupation numbers saturate (or nearly saturate) the generalized Pauli constraints, then the occupation numbers are said to be pinned (or quasi-pinned) to the constraints. Here, we assess the complexity of electron correlation of excited states from the pinning or quasi-pinning of the occupation numbers to the generalized Pauli constraints where the degree of pinning encodes information about the structure of the wave function including correlation and entanglement. Results are presented for three-and fourelectron atoms and molecules, the five-electron cyclopentadienyl radical, and the seven-electron Fenna-Matthews-Olson complex in green-sulfur bacteria. The data shows that even when the ground-state occupation numbers are pinned, the occupation numbers of excited states manifest pinned, quasipinned, and unpinned behavior, reflecting the complexity of electron correlation and entanglement in excited states. V C

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Structure of the one‐electron reduced density matrix from the generalized Pauli exclusion principle

Cited by 22 publications

References 51 publications

Optimal Slater-determinant approximation of fermionic wave functions

Optimal Slater-determinant approximation of fermionic wave functions

Generalized Pauli constraints in small atoms

Role of the generalized pauli constraints in the quantum chemistry of excited states

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