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Ground state and excitation spectra of a strongly correlated lattice by the coupled cluster method.

Alessandro Mirone

Published Jan 1, 2012• 2 citations
OpenAlex

Abstract

We apply Coupled Cluster Method to a strongly correlated lattice Hamil-tonian and we extend the Coupled Cluster linear response method to the cal-culation of electronic spectra. We do so by finding an approximation to a re-solvent operator which describes the spectral response of the Coupled Cluster solution to excitation operators. In our Spectral Coupled Cluster Method the ground and excited states appear as resonances in the spectra and the resol-vent can be iteratively improved in selected spectral regions. We apply our method to a MnO2 plane model which corresponds to previous experimental works. 1

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Europhysics Letters (EPL)•Feb 1, 1990•47 citations
We apply Coupled Cluster Method to a strongly correlated lattice Hamil-tonian and we extend the Coupled Cluster linear response method to the cal-culation of electronic spectra. We do so by finding an approximation to a re-solvent operator which describes the spectral response of the Coupled Cluster solution to excitation operators. In our Spectral Coupled Cluster Method the ground and excited states appear as resonances in the spectra and the resol-vent can be iteratively improved in selected spectral regions. We apply our method to a MnO2 plane model which corresponds to previous experimental works. 1
The coupled cluster method is applied to a strongly correlated lattice Hamiltonian, and the coupled cluster linear response method is extended to the calculation of electronic spectra by finding an approximation to a resolvent operator which describes the spectral response of the coupled cluster solution to excitation operators. In this spectral coupled cluster method, the ground and excited states appear as resonances in the spectra, and the resolvent can be iteratively improved in selected spectral regions. The method is applied to a MnO(2) plane model which corresponds to previous experimental works.
The Spectral Coupled Cluster Method with kkk dependency for strongly correlated lattices
We adapt the Coupled Cluster Method to solid state strongly correlated lattice Hamiltonians extending the Coupled Cluster linear response method to the calculation of electronic spectra and obtaining the space-time Fourier transforms of generic Green's functions. We apply our method to the MnO2MnO_2MnO2​ plane with orbital and magnetic ordering, to interpret electron energy loss experimental data, and to the Hubbard model, where we get insight into a possible pairing mechanism.
We present a coupled cluster method (CCM) with optimized excitation operators. The efficiency comes from a parameterized form of excitation operators. The parameters are found by variational optimization procedure. The resultant number of excitation operators is much smaller than that of the conventional CCM theory. This property makes it possible to apply the method in systems of solid state physics. Starting from Hartree-Fock state as the reference state, i.e., the Fermi sea, we search for particle-hole excitation operators such that the wave function of configuration interaction in terms of these excitation operators spans a good approximation to the ground state. The Match-pursuit algorithm is capable of doing the search of the excitation operators. The resultant operators are our excitation operators for the CCM wave function. We test the method by two dimensional fermionic Hubbard model on a square lattice.
The coupled-cluster method is applied to the spin-1/2 antiferromagnetic XXZ model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, the sublattice magnetization and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.
High-Order Coupled Cluster Method (CCM) Formalism 1: Ground- and Excited-State Properties of Lattice Quantum Spin Systems with s>=1/2s >= 1/2s>=1/2
The coupled cluster method (CCM) is a powerful and widely applied technique of modern-day quantum many-body theory. It has been used with great success in order to understand the properties of quantum magnets at zero temperature. This is due largely to the application of computational techniques that allow the method to be applied to high orders of approximation using localised approximation schemes, e.g., such as the LSUBmmm scheme. In this article, the high-order CCM formalism for the ground and excited states of quantum magnetic systems are extended to those with spin quantum number s≥12s \ge \frac 12s≥21​. Solution strategies for the ket- and bra-state equations are also considered. Aspects of extrapolation of CCM expectation values are discussed and future topics regarding extrapolations are presented.
The coupled-cluster approximation (CCA) is applied to the ground state of strongly interacting fermions or spins on a regular lattice. A new scheme of successive CCAs, suitable for the lattice problem is proposed. Excellent approximations of the ground-state energies are obtained at the lowest levels in a straightforward way. Two examples are given: the antiferromagnetic Heisenberg linear chain and the half-filled Hubbard model on a two-dimensional square lattice, with comparison to exact results and/or other approximations.