Generalization of group-theoretic coherent states for variational calculations

We introduce families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan subalgebra elements and by applying these unitaries to regular group-theoretic coherent states. This enables us to generate entanglement not found in the coherent states themselves, while retaining many of their desirable properties. Most importantly, we explain how the expectation values of physical observables can be evaluated efficiently. Examples include generalized spin-coherent states and generalized Gaussian states, but our construction can be applied to any Lie group represented on the Hilbert space of a quantum system. We comment on their applicability as variational families in condensed matter physics and quantum information.

Automated summary

This study introduces families of pure quantum states by constructing operators and applying them to regular coherent states, generating entanglement not found in the coherent states themselves while preserving their desirable properties. It also explains how to efficiently evaluate the expectation values of physical observables and discusses the applicability of these states in condensed matter physics and quantum information as variational families.