A time-dependent formulation of coupled cluster theory for many-fermion systems at finite temperature

TL;DR

This paper introduces a time-dependent coupled cluster theory for finite-temperature quantum systems, enabling direct free energy calculations and efficient response property evaluations, with applications demonstrated on warm dense matter.

Contribution

It develops a finite-temperature coupled cluster framework based on imaginary time integration, connecting it to perturbation and zero-temperature theories, and demonstrates its implementation for realistic systems.

Findings

Successfully derived finite-temperature CC singles and doubles equations

Enabled efficient computation of response properties using a variational Lagrangian

Applied method to calculate exchange correlation energy in warm dense matter

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.