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

Abstract

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.

The Spin-Partitioned Total-Position Spread Tensor: An Application To Diatomic Molecules

“…In this work we have reported a study of the dependence of the SP-TPS tensor on the internuclear distance for a selected set of diatomic molecules, which complements a similar work on the SS-TPS tensor and the analysis of the behavior of the SP-TPS tensor in other systems, in particular, open-shell systems. , …”

“…The LT is also an indicator of the square of the exchange-correlation lengths in the electronic distribution, which refers to the influence of one electron on the other electrons . A few examples of the evaluation of this quantity for various molecular systems have been presented by the present authors ,− and by others (see ref and references therein).…”

“…In this work we have reported a study of the dependence of the SP-TPS tensor on the internuclear distance for a selected set of diatomic molecules, which complements a similar work on the SS-TPS tensor 18 and the analysis of the behavior of the SP-TPS tensor in other systems, in particular, open-shell systems. 15,16 We have illustrated this point by applying the formalism to a few light diatomic molecules, ranging from covalent (H 2 , Li 2 , and N 2 ), charge-shift (F 2 ), and ionic (LiF) bonds to weakly bonded systems like He 2 and Be 2 . The present results show the ability of the SP-TPS tensor to give interesting information not only about molecular systems with unpaired electrons (where the spin delocalization can reasonably be expected to play a key role) as discussed in previous works but also in the case of "ordinary" molecules, in particular, when the bonds are stretched, leading to an openshell electronic distribution.…”

A Wigner molecule at extremely low densities: a numerically exact study

“…[29]). The localization tensor has been applied to study the metallic behavior of clusters [30][31][32][33][34][35][36][37][38], chemical bonding [39] and electron transport. [40] It has recently also been used to investigate Wigner localization.…”

Signatures of Wigner localization in one-dimensional systems

“…For this reason, a qualitatively different behavior of the localization tensor is expected in the Fermi-liquid and Wigner-crystal regimes of the electron gas. The localization tensor has been used to investigate the metallic behavior of finite clusters, both at ab initio [26][27][28] and semi-empirical [29][30][31][32][33][34] level.…”