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

**Authors:** Alec F. White, Garnet Chan  
**arXiv:** [1807.09961](https://arxiv.org/abs/1807.09961)  
**Date:** 2018-07-26  
**Summary page:** https://www.summarizepaper.com/en/paper/1807.09961v2/

## Key points

- White and Chan present a new approach to computing the free energy of quantum systems at finite temperature using a time-dependent formulation of coupled cluster theory.
- The method involves imaginary time integration and is related to thermal cluster cumulant theory.
- The authors provide a detailed derivation of the method, highlighting its connection to perturbation theory and zero-temperature coupled cluster theory.
- They demonstrate how the finite-temperature coupled cluster singles and doubles amplitude equations can be derived in analogy with the zero-temperature theory.
- Response properties can be efficiently computed using a variational Lagrangian.
- The implementation of this method for realistic systems is discussed, with particular emphasis on its potential utility in calculating the exchange correlation energy of the uniform electron gas at warm dense matter conditions.
- The authors showcase their approach through calculations that accurately predict thermodynamic properties of complex quantum systems.

## Summary

In their paper titled "A time-dependent formulation of coupled cluster theory for many-fermion systems at finite temperature," Alec F. White and Garnet Chan present a novel approach to computing the free energy of quantum systems at finite temperature using a time-dependent formulation of coupled cluster theory. The method involves imaginary time integration and is closely related to the thermal cluster cumulant theory developed by Mukherjee and co-workers. The authors provide a detailed derivation of the method, highlighting its connection to perturbation theory and zero-temperature coupled cluster theory. They demonstrate how the finite-temperature coupled cluster singles and doubles amplitude equations can be derived in analogy with the zero-temperature theory, and show how response properties can be efficiently computed using a variational Lagrangian. The implementation of this method for realistic systems is discussed, with particular emphasis on its potential utility in calculating the exchange correlation energy of the uniform electron gas at warm dense matter conditions. To illustrate its effectiveness, the authors showcase their approach through calculations that accurately predict thermodynamic properties of complex quantum systems. Overall, this paper presents an innovative approach to tackling one of the most challenging problems in computational physics – computing free energies at finite temperature – and provides valuable insights into how this problem can be addressed using advanced mathematical techniques such as coupled cluster theory.