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APS

Exact Diagonalization of Various Strongly Correlated Models of High-Temperature Superconductivity in Cubic and Octahedral Atomic Clusters.

Hüseyin Boyacı, I. Kulik

Published Mar 1, 1997• 0 citations
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Towards lattice-gas description of low-temperature properties above the Haldane and cluster-based Haldane ground states of a mixed spin-(1,1/2) Heisenberg octahedral chain

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The rich ground-state phase diagram of the mixed spin-(1,1/2) Heisenberg octahedral chain was previously elaborated from effective mixed-spin Heisenberg chains, which were derived by employing a local conservation of a total spin on square plaquettes of an octahedral chain. Here we present a comprehensive analysis of the thermodynamic properties of this model. In the highly frustrated parameter region the lowest-energy eigenstates of the mixed-spin Heisenberg octahedral chain belong to flat bands, which allow a precise description of low-temperature magnetic properties within the localized-magnon approach exploiting a classical lattice-gas model of hard-core monomers. The present article provides a more comprehensive version of the localized-magnon approach, which extends the range of its validity down to a less frustrated parameter region involving the Haldane and cluster-based Haldane ground states. A comparison between results of the developed localized-magnon theory and accurate numerical methods such as full exact diagonalization and finite-temperature Lanczos technique convincingly evidence that the low-temperature magnetic properties above the Haldane and the cluster-based Haldane ground states can be extracted from a classical lattice-gas model of hard-core monomers and dimers, which is additionally supplemented by a hard-core particle spanned over the whole lattice representing the gapped Haldane phase.

arXiv:2203.11569•Physical review. E•Jul 8, 2022•5 citations
The numerical method was developed that combines the variational cluster approximation and the exact diagonalization techniques to solve Hubbard models of various dimensionality, number of orbitals, and lattice geometry. The developed method was tested on the one-band Hubbard model; antiferromagnetic ordering and the superconducting phase were observed, in accordance with known results obtained by other techniques. The method may be successfully used for studying properties of high-temperature superconductors.
A review of the physical properties of small systems described by various model Hamiltonians is given. Their physical properties are found either exactly or by using Monte-Carlo methods, and are compared with properties of bulk systems. It is shown that (i) clusters differ in an essential way from the bulk, having electronic states strongly dependent on the geometry and cluster size, but, at the same time, (ii) important insights into the nature of electron correlation and low-energy excitations in solids may be gained by cluster studies. In particular, the cluster calculations allow one to identify the tendencies to various kinds of symmetry-broken states in the (extended) Hubbard model and give a simple qualitative understanding of the low temperature properties of the Kondo and the heavy-fermion systems. Furthermore, cluster calculations allow one to study such problems as the development of magnetic moment at chemisorbed atoms for strong correlations and the suppression of frustration by quantum fluctuations. Recently, cluster calculations gave important information about the possible role of charge transfer processes and magnetic interactions in the microscopic mechanism of pairing in high temperature superconducting oxides.
The rich ground-state phase diagram of the mixed spin-(1,1/2) Heisenberg octahedral chain was previously elaborated from effective mixed-spin Heisenberg chains, which were derived by employing a local conservation of a total spin on square plaquettes of an octahedral chain. Here we present a comprehensive analysis of the thermodynamic properties of this model. In the highly frustrated parameter region the lowest-energy eigenstates of the mixed-spin Heisenberg octahedral chain belong to flat bands, which allow a precise description of low-temperature magnetic properties within the localized-magnon approach exploiting a classical lattice-gas model of hard-core monomers. The present article provides a more comprehensive version of the localized-magnon approach, which extends the range of its validity down to a less frustrated parameter region involving the Haldane and cluster-based Haldane ground states. A comparison between results of the developed localized-magnon theory and accurate numerical methods such as full exact diagonalization and finite-temperature Lanczos technique convincingly evidence that the low-temperature magnetic properties above the Haldane and the cluster-based Haldane ground states can be extracted from a classical lattice-gas model of hard-core monomers and dimers, which is additionally supplemented by a hard-core particle spanned over the whole lattice representing the gapped Haldane phase.