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The coupled cluster method applied to quantum magnetism

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Quantum Magnetism

Part of the book series: Lecture Notes in Physics ((LNP,volume 645))

Abstract

The Coupled Cluster Method (CCM) is one of the most powerful and universally applied techniques of quantum many-body theory. In particular, it has been used extensively in order to investigate many types of lattice quantum spin system at zero temperature. The ground-and excited-state properties of these systems may now be determined routinely to great accuracy. In this Chapter we present an overview of the CCM formalism and we describe how the CCM is applied in detail. We illustrate the power and versatility of the method by presenting results for four different spin models. These are, namely, the XXZ model, a Heisenberg model with bonds of differing strengths on the square lattice, a model which interpolates between the Kagomé-and triangular-lattice antiferromanets and a frustrated ferrimagnetic spin system on the square lattice. We consider the ground-state properties of all of these systems and we present accurate results for the excitation energies of the spin-half square-lattice XXZ model. We utilise an “extended” SUB2 approximation scheme, and we demonstrate how this approximation may be solved exactly by using Fourier transform methods or, alternatively, by determining and solving the SUB2-m problem. We also present the results of “localised” approximation schemes called the LSUBm or SUBm-m schemes. We note that we must utilise computational techniques in order to solve these localised approximation schemes to “high order.” We show that we are able to determine the positions of quantum phase transitions with much accuracy, and we demonstrate that we are able to determine their quantum criticality by using the CCM in conjunction with the coherent anomaly method (CAM). Also, we illustrate that the CCM may be used in order to determine the “nodal surfaces” of lattice quantum spin systems. Finally, we show how connections to cumulant series expansions may be made by determining the perturbation series of a spin-half triangular-lattice antiferromagnet using the CCM at various levels of LSUBm approximation.

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Authors and Affiliations

  1. Unit of Ophthalmology, Department of Medicine University Clinical Departments, University of Liverpool, Daulby Street, L69 3GA, Liverpool, UK

    Damian J. J Farnell

  2. Department of Physics, University of Manchester Institute of Science and Technology (UMIST), P.O. Box 88, M60 1QD, Manchester, UK

    Raymond F. Bishop

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Ulrich Schollwöck Johannes Richter Damian J. J. Farnell Raymod F. Bishop

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Farnell, D.J.J., Bishop, R.F. (2004). The coupled cluster method applied to quantum magnetism. In: Schollwöck, U., Richter, J., Farnell, D.J.J., Bishop, R.F. (eds) Quantum Magnetism. Lecture Notes in Physics, vol 645. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0119597

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