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Springer eBooks

Extended Coupled Cluster Techniques for Excited States: Applications to Quasispin Models

R. F. Bishop, N. I. Robinson, J. Arponen

Published Jan 1, 1990• 1 citation
Publisher
DOI
10.1007/978-1-4613-0605-4_34

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Earlier papers in this series have shown how the extended coupled-cluster method (ECCM) provides a widely applicable biorthogonal formulation of quantum many-body and quantum field theory. Rules for calculating matrix elements of arbitrary operators have been formulated, and an exact description of the excited states has been given in terms of a generalized random-phase approximation for the many-body, quasilocal c-number (classical), ECCM cluster amplitudes which completely and exactly parametrize the system. The present paper introduces a variational functional in order to treat the excited states differently within the ECCM framework, so as to allow extra flexibility in the choice of approximation schemes. The method is tested on the SU(2) quasispin model of Lipkin, Meshkov, and Glick [Nucl. Phys. 62, 188 (1965); 62, 199 (1965)], which contains the spontaneous breakdown of parity, and which models a shape transition in finite atomic nuclei. The method very well describes both the ground and excited states of the model Hamiltonian over a broad range of coupling parameters on both sides of the critical value corresponding to the transition.
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.