A Time-Dependent Formulation of Coupled-Cluster Theory for Many-Fermion Systems at Finite Temperature

Abstract

We present a time-dependent formulation of coupled cluster theory. This theory allows for direct computation of the free energy of quantum systems at finite temperature by imaginary time integration and is closely related to the thermal cluster cumulant theory of Mukherjee and co-workers. Our derivation highlights the connection to perturbation theory and zero-temperature coupled cluster theory. We show explicitly how the finite-temperature coupled cluster singles and doubles amplitude equations can be derived in analogy with the zero-temperature theory and how response properties can be efficiently computed using a variational Lagrangian. We discuss the implementation for realistic systems and showcase the potential utility of the method with calculations of the exchange correlation energy of the uniform electron gas at warm dense matter conditions. arXiv:1807.09961v2 [physics.chem-ph]

Thermofield Theory for Finite-Temperature Coupled Cluster

“…Next, we consider the reduced BCS or the pairing model, the Hamiltonian for which is given by 30) where N p counts the number of electrons, p denotes the energy, and P † p /P p respectively creates/annihilates a pair of electrons in the p th -level, while G quantifies the attractive pair-hopping interaction. Here we choose the energy levels with a uniform spacing of 1 unit, i.e., ∆ = p+1 − p = 1.…”

Time-Dependent Coupled Cluster Theory on the Keldysh Contour for Nonequilibrium Systems

“…The implementation of Keldysh-CCSD closely mirrors the implementation of FT-CCSD, so we refer to Ref. 49 for most of the details. There are two primary differences.…”

“…We will not derive these theories in detail, as they can be found elsewhere (see for example Ref. 49), but they are most easily considered from a diagrammatic perspective. The 0th and 1st order perturbation theory contributions are trivial, and are not considered here.…”

“…We work within the density matrix language, and use the Keldysh formalism [55][56][57] to provide a straightforward generalization of the imaginary-time finite-temperature CC equations in Ref. 49 to describe the dynamics of finite temperature systems. We show some initial applications to model systems and a simple ab initio representation of high-temperature silicon under the influence of an ultrafast extreme ultraviolet (XUV) pulse.…”

“…Finite temperature coupled cluster In Ref. 49 we presented a finite temperature coupled cluster theory which provides an ansatz for the correlation contribution to the grand potential Ω such that Ω = Ω (0) + Ω (1) + Ω CC (1) where Ω (0) + Ω (1) is the grand potential of the thermal Hartree-Fock theory and Ω CC is the approximation computed by coupled cluster. Our strategy was to generalize the diagrammatic rules of finite temperature perturbation theory to the diagrammatic representation of the coupled cluster iteration.…”