What has since become known as the normal coupled cluster method (NCCM) was invented about thirty years ago to calculate ground-state energies of closed-shell atomic nuclei. Coupled cluster (CC) techniques have since been developed to calculate excited states, energies of open-shell systems, density matrices and hence other properties, sum rules, and the sub-sum-rules that follow from imbedding linear response theory within the NCCM. Further extensions deal both with systems at nonzero temperature and with general dynamical behaviour. More recently, a new version of CC theory, the so-called extended coupled cluster method (ECCM) has been introduced. It has the potential to describe such global phenomena as phase transitions, spontaneous symmetry breaking, states of topological excitation, and nonequilibrium behaviour. CC techniques are now widely recognized as providing one of the most universally applicable, most powerful, and most accurate of all microscopicab initio methods in quantum many-body theory. The number of successful applications within physics is now impressively large. In most such cases the numerical results are either the best or among the best available. A typical case is the electron gas, where the CC results for the correlation energy agree over the entire metallic density range to within less than 1 millihartree (or <1%) with the essentially exact Green's function Monte Carlo results. The role of CC theory within modern quantum many-body theory is first surveyed, by a comparison with other techniques. Its full range of applications in physics is then reviewed. These include problems in nuclear physics, both for finite nuclei and infinite nuclear matter; the electron gas; various integrable and nonintegrable models; various relativistic quantum field theories; and quantum spin chain and lattice models. Particular applications of the ECCM include the quantum hydrodynamics of a zero-temperature, strongly-interacting condensed Bose fluid; a charged impurity in a polarizable medium (e.g., positron annihilation in metals); and various anharmonic oscillator and spin systems.

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An overview of coupled cluster theory and its applications in physics

Nucleonic superfluidity in neutron stars: 1S0 neutron pairing in the inner crust

The origins of the coupled cluster method are described. Special attention is paid to the arguments put forward for the exponential structure of the wave functions. Various approximation schemes invented during the last 40 years are presented. The problems arising from these approximations necessarily truncating or destroying the exponential form are discussed and ways to deal with them are described.

A biography of the coupled cluster method

Variations on the electron gas

The coupled cluster method (CCM) is nowadays widely recognised as providing one of the most powerful, most universally applicable, and numerically most accurate at attainable levels of implementation, of all available ab initio methods of microscopic quantum many-body theory. The number of successful applications of the method to a wide range of physical and chemical systems is impressively large. In almost all such cases the numerical results are either the best or among the best available. A typical example is the electron gas, where the CCM results for the correlation energy agree over the entire metallic density range to within less than one millihartree per electron (or <1%) with the essentially exact Green?s function Monte Carlo results. What has since become known as the normal (NCCM) version of the method was invented some forty years ago to calculate the ground-state energies of closed-shell atomic nuclei. Extensions of the CCM have since been developed to calculate excited states, energies of open-shell systems, density matrices and hence other properties, sum rules, and the sub-sum-rules that follow from embedding linear response theory within the NCCM. Further extensions deal with the general dynamics of quantum many-body systems, and with their mixed states appropriate, for example, to their behaviour at nonzero temperatures. More recently, a so-called extended (ECCM) version of the method has been introduced. It has the same ability as the NCCM to describe accurately the local properties of quantum many-body systems, but it also has the potential to describe such global phenomena as phase transitions, spontaneous symmetry breaking, states of topological excitation, and nonequilibrium behaviour. The role of the CCM within modern quantum many-body theory is first surveyed, by a comparison with, and discussion of, the alternative microscopic formulations. We then discuss the method and each of its individual components in considerable detail. Our overall aim is to stress the broad applicability of the method. To that end we introduce and exploit a very general theoretical framework in which to formulate the key ideas and to develop the theory. We end with a brief review of the applications of the method to date.

E. Krotscheck

Papers

Coupled-cluster many-body theory in a correlated basis