Finite temperature coupled cluster theories for extended systems

TL;DR

This paper develops a finite temperature coupled cluster theory for extended systems, using an imaginary time domain approach that is computationally efficient and allows benchmarking against zero-temperature results.

Contribution

It introduces a numerically efficient imaginary time domain method for finite temperature coupled cluster calculations applicable to extended systems.

Findings

Finite temperature coupled cluster free energies computed for lithium and silicon.

The method achieves high accuracy with about a dozen grid points.

The approach seamlessly connects finite and zero temperature regimes.

Abstract

At zero temperature coupled cluster theory is widely used to predict total energies, ground state expectation values and even excited states for molecules and extended systems. Generalizations to finite temperature exist, however, they are in practice several orders of magnitude more demanding compared to the zero temperature case since the amplitudes must be computed and stored for many Matsubara frequencies to yield sufficiently accurate results. Instead of using Matsubara frequencies one can also work directly in the imaginary time domain on the compact interval [0, beta]. The arising imaginary time dependent coupled cluster amplitude integral equations are solved numerically on a non-uniform grid. About a dozen grid points provide sufficient accuracy if the Hamiltonian is repartitioned to include particle/hole interactions in the non-perturbative part. In this framework the transition from finite to zero temperature is uniform and comes at no extra costs, allowing, for instance, to benchmark fractional occupancy formulations of coupled cluster theories. Finite temperature direct ring coupled cluster doubles free energies are calculated for various temperatures for solid lithium, a metallic system, and for solid silicon, a semiconductor.