Symmetry-Restored Coupled-Cluster Theory
- Thomas Duguet, CEA/IRFU/SPhN
Tuesday, March 11, 11:00 AM - Theory Seminar
NSCL Seminar Room
Very recently, self-consistent Green's function theory, in-medium similarity renormalization group techniques and coupled-cluster theory have been extended to describe (singly) open-shell mid-mass nuclei in an ab initio fashion for the first time. The extension of quantum many-body methods to open-shell systems constitutes a long-standing difficulty as it requires to expand the many-body solution around a near-degenerate reference state. One way to overcome this quasi-degeneracy problem relies on the development of multi-reference methods. To a large extent, this has been the route followed in quantum chemistry over the last thirty years and by the in-medium similarity renormalization group techniques in the nuclear context.
There exists an alternative strategy that exploits the concept of spontaneous symmetry breaking in order to commute the degeneracy of the reference state with respect to particle-hole excitations into a degeneracy with respect to transformations of the associated symmetry group, i.e. it produces a Goldstone mode in the manifold of closed-shell product states connected via symmetry transformations. This trade off allows one to take a good first shot at open-shell systems on the basis of a single-reference method, while postponing the handling of the Golstone mode to a later stage. This idea has been recently exploited to address singly open-shell nuclei through symmetry-unrestricted Greenís function and coupled-cluster techniques. However, the description is achieved in this way at the price of losing good symmetry quantum numbers. Eventually, the degeneracy associated with the Goldstone mode must be resolved given that the symmetry breaking is in fact only fictitious in finite systems.
In this context, I will present the first generic formulation of symmetry restoration within coupled cluster theory, trying to underline the key difficulties that needed to be overcome and the solutions that have been identified to achieve this goal.