Spin delocalization in hydrogen chains described with the spin-partitioned total position-spread tensor

Khatib, Muammar El; Brea, Oriana; Fertitta, Edoardo; Bendazzoli, Gian Luigi; Evangelisti, Stefano; Leininger, Thierry; Paulus, Beate

doi:10.1007/s00214-015-1625-7

Cited by 10 publications

(11 citation statements)

References 40 publications

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“…They have been the object of a separate investigation. 28 The case of Hubbard open chains has been numerically investigated at FCI level. These chains are extremely well studied systems, both analytically and numerically.…”

Section: Introductionmentioning

confidence: 99%

The total position-spread tensor: Spin partition

Khatib

Brea

Fertitta

et al. 2015

The Journal of Chemical Physics

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The Total Position Spread (TPS) tensor, defined as the second moment cumulant of the position operator, is a key quantity to describe the mobility of electrons in a molecule or an extended system. In the present investigation, the partition of the TPS tensor according to spin variables is derived and discussed. It is shown that, while the spin-summed TPS gives information on charge mobility, the spin-partitioned TPS tensor becomes a powerful tool that provides information about spin fluctuations. The case of the hydrogen molecule is treated, both analytically, by using a 1s Slater-type orbital, and numerically, at Full Configuration Interaction (FCI) level with a V6Z basis set. It is found that, for very large inter-nuclear distances, the partitioned tensor growths quadratically with the distance in some of the low-lying electronic states. This fact is related to the presence of entanglement in the wave function. Non-dimerized open chains described by a model Hubbard Hamiltonian and linear hydrogen chains H n (n ≥ 2), composed of equally spaced atoms, are also studied at FCI level. The hydrogen systems show the presence of marked maxima for the spin-summed TPS (corresponding to a high charge mobility) when the inter-nuclear distance is about 2 bohrs. This fact can be associated to the presence of a Mott transition occurring in this region. The spin-partitioned TPS tensor, on the other hand, has a quadratical growth at long distances, a fact that corresponds to the high spin mobility in a magnetic system. C 2015 AIP Publishing LLC. [http://dx

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Section: Introductionmentioning

confidence: 99%

The total position-spread tensor: Spin partition

Khatib

Brea

Fertitta

et al. 2015

The Journal of Chemical Physics

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“…The general formalism of the spin-partitioned TPS tensor is fully unfolded in our previous works on the H 2 molecule 16 and hydrogen chains. 25 In the present paper, we summarize its main aspects and describe its application to the special case of Heisenberg chains. Indicating byr(i), the vector operator associated to the position of electron i, it is possible to define the total position operator as the many-body operator given by the sum of all the individual electron-position operators,…”

Section: The Spin Partition Of Tps Tensor For the Heisenberg Wavmentioning

confidence: 99%

“…These wave functions present very different SP-TPS values which, for a fixed value of n, show a quadratic dependence on the quantum number m, having a maximum for m = 0 and being zero for m = ±s. In order to ease the comparison between the different chains, it is a common practice to normalize the TPS to the number of sites 16,25 as done in Figure 3, where the values of the λ n 2 , m αα = Λ n 2 , m αα /n are reported as a function of m for different number of sites (the values can be found in Table III of the supplementary material 38 ). As explained in detail in Appendix B, the αα spin partitioned component obeys to the following law:…”

Section: Ferromagnetic Casementioning

confidence: 99%

“…As already stated, the Heisenberg wave function for the spin-paired chains can be used as a model to describe the behavior of the coupled spins in a dimerized hydrogen chain where we observe a Peierls transition. 25 The dimensionless real parameter η = J 2 /J 1 was used to define the degree of spin-pairing: we have η = 1 for the equal-J chains, and η < 1 in presence of dimerization. In the limit case of η = 0 the system is composed of n/2 non-interacting spin pairs.…”

Section: B Spin-paired Chainsmentioning

confidence: 99%

“…Despite the fact that the TPS tensor has been subject of a variety of works in the last years, [13][14][15][17][18][19][20][21][22][23][24] the spinpartitioned TPS (SP-TPS) formalism is a new tool which has been introduced in our recent works on H 2 molecule 16 and hydrogen chains (H n ), 25 where we showed in detail how it allows to investigate separately the fluctuations of the same-spin and different-spin electrons in a system. In the present work, we focus our attention on the spin part of the wave function of linear systems, through the use of the Heisenberg model Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

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The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains

Fertitta

Khatib

Bendazzoli

et al. 2015

The Journal of Chemical Physics

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The spin partition of the Total Position-Spread (TPS) tensor has been performed for one-dimensional Heisenberg chains with open boundary conditions. Both the cases of a ferromagnetic (high-spin) and an anti-ferromagnetic (low-spin) ground-state have been considered. In the case of a low-spin ground-state, the use of alternating magnetic couplings allowed to investigate the effect of spin-pairing. The behavior of the spin-partitioned TPS (SP-TPS) tensor as a function of the number of sites turned to be closely related to the presence of an energy gap between the ground-state and the first excited-state at the thermodynamic limit. Indeed, a gapped energy spectrum is associated to a linear growth of the SP-TPS tensor with the number of sites. On the other hand, in gapless situations, the spread presents a faster-than-linear growth, resulting in the divergence of its per-site value. Finally, for the case of a high-spin wave function, an analytical expression of the dependence of the SP-TPS on the number of sites n and the total spin-projection Sz has been derived.

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