Quantum Spin Lattice Models: A Coupled-Cluster Treatment

DAMIAN J. J. FARNELL, JB Parkinson

C. H. Woo

R. F. Bishop, Yang Xian, Chen Zeng

Abstract We recently applied the coupled‐cluster method (CCM) with considerable success to several novel quantum spin‐lattice systems in the infinite bulk limit. In this article, we extend our CCM analysis to the electronic Hubbard models. In particular, based on a systematic approximation scheme within the CCM, we investigate the zero‐temperature properties of Hubbard models at half‐filling and with a single hole on a general bipartite lattice. Our aim was to provide the CCM framework for a systematic calculation of the properties of Hubbard models. © 1995 John Wiley & Sons, Inc.

R. F. Bishop, John B. Parkinson, Yang Xian

The coupled-cluster method (CCM) is applied to anisotropic-quantum-antiferromagnetic models in one and two dimensions (1D and 2D). Several hierarchical approximation schemes of the CCM are defined, which are specialized for the spin-lattice models. Good results are obtained for both ground-state and excited-state energies. The spin-spin correlation functions and the staggered magnetizations are also calculated. We have found that the CCM gives a qualitatively correct description of the entire Heisenberg-Ising phase, including the critical point where a phase transition occurs in 1D. Some interesting differences between 1D and 2D models near the critical point are discussed.

Marco Vekić

M. Georgiou, Ioannis Rousochatzakis, DAMIAN J. J. FARNELL +2 more

We study the spin- S Kitaev-Heisenberg model on the honeycomb lattice for S = 1 / 2 , 1, and 3 / 2 , by using the coupled cluster method (CCM) of microscopic quantum many-body theory. This system is one of the earliest extensions of the Kitaev model and is believed to contain two extended spin liquid phases for any value of the spin quantum number S . We show that the CCM delivers accurate estimates for the phase boundaries of these spin liquid phases, as well as other transition points in the phase diagram. Moreover, we find evidence of two unexpected narrow phases for S = 1 / 2 , one sandwiched between the zigzag and ferromagnetic phases and the other between the Néel and the stripy phases. The results establish the CCM as a versatile numerical technique that can capture the strong quantum-mechanical fluctuations that are inherently present in generalized Kitaev models with competing bond-dependent anisotropies. Published by the American Physical Society 2024