Extended coupled-cluster method. II. Excited states and generalized random-phase approximation

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Abstract
This article gives a discussion of the application of the extended coupled-cluster method (ECCM) to the excited states of a general quantum many-body system. The direct eigenvalue equations for the excitation amplitudes of both the ket and the bra eigenstates are derived in the biorthogonal basis obtained by a double similarity transformation. The equations correspond to the diagonalization of a matrix involving second-order functional derivatives of the average-value functional for the Hamiltonian with respect to the basic ECCM amplitudes. The same excitation spectrum is obtained by considering small oscillations around the equilibrium. The problem with its associated effective Hamiltonian has the structure of a generalized random-phase approximation. By diagonalizing the effective Hamiltonian we perform a canonical or symplectomorphic coordinate transformation into normal coordinates in the symplectic ECCM phase space. In this coordinate system the exact average-value functional for the Hamiltonian has a structure analogous to that of classical lattice dynamics or the phenomenological Ginzburg-Landau theory. At all stages the method satisfies the property of quantum locality, which in real space shows up as a definite quasilocality. Due to this property the method allows, for example, the treatment of mesonlike excitations in the presence of topological objects or in other symmetry-broken equilibrium states.