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Non-classical correlations in a Heisenberg spin model with Heitler–London approach

Youssef Khedif, Saeed Haddadi, Mohammed Daoud A, Hazhir Dolatkhah, Mohammad Reza Pourkarimi

Published Jun 30, 2022• 18 citations
Publisher
DOI
10.1007/s11128-022-03565-y

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Abstract This study investigates the dynamics of quantum coherence and entanglement in the spin‐1 Heisenberg XXZ model. Particularly, the effects of the Heitler‐London (HL) coupling and the Dzyaloshinskii‐Moriya (DM) interaction are examined. By utilizing tools from quantum information theory, the concept of quantum correlated coherence and negativity are explored. The results show intrinsic decoherence leads to a decay of both correlated coherence and negativity. Interestingly, it is found that a small value of the Dzyaloshinskii‐Moriya interaction can significantly enhance coherence and entanglement. Various factors influence the system dynamics, including the initial state, anisotropy parameter, and the coupling distance between spins. It is shown that, by fixing the anisotropy parameter, the isotropic Heisenberg models XX and XXX can be easily recovered. Ultimately, the findings highlight that the system maintains a coherent temporal evolution despite decoherence.
One- and two-particle reduced density matrices have been calculated for a ``resonating'' Heitler-London wavefunction, in a system which is a finite model of a two-dimensional square planar lattice structure (4×4 net of one-electron atoms with Born-von Karman boundary conditions). The Heitler-London wavefunction describes the electronic ground state of a system with a single narrow half-filled band (the Mott insulator). Various measures of electron correlation (pair correlation functions, etc.) are defined and calculated. The intent of these calculations is to provide ``empirical'' guidelines for many-body methods for calculation of Green's functions for one and two particles (reduced density matrices are initial values for the respective Green's functions). Results show that the Heitler-London description is incompatible with several assumptions and widely used models for the Mott insulator. In particular it is found that (a) pair correlations in the Heitler-London ground state remain local even when ``resonance'' of an extremely large number of valence-bond structures occurs; the long range antiferromagnetic ordering obtained in several models of the Mott insulator (the ``two-sublattice'' or ``different bands for different spins'' models) does not occur. (b) The density matrix for the Heitler-London state does not exhibit a BCS type ``pair condensation'', as has been conjectured to describe the Mott insulator in some recent work. Our results strongly suggest that if the Heitler-London description is appropriate, the ``Hubbard Hamiltonian'', which includes only intraatomic pair interactions, does not offer an adequate model of the Mott insulator.