Conservation laws in coupled cluster dynamics at finite-temperature

TL;DR

This paper extends finite-temperature non-equilibrium coupled cluster theory to include a time-dependent orbital basis, ensuring conservation laws and demonstrating its effectiveness on various non-equilibrium quantum systems.

Contribution

It introduces a time-dependent orbital-optimized coupled cluster doubles method at finite temperature, preserving conservation laws and expanding the applicability of coupled cluster dynamics.

Findings

Restores local and global conservation laws in finite-temperature dynamics.

Demonstrates energy conservation for time-independent Hamiltonians.

Shows numerical effectiveness on multiple non-equilibrium quantum models.

Abstract

We extend the finite-temperature Keldysh non-equilibrium coupled cluster theory (Keldysh-CC) [{\it J. Chem. Theory Comput.} \textbf{2019}, 15, 6137-6253] to include a time-dependent orbital basis. When chosen to minimize the action, such a basis restores local and global conservation laws (Ehrenfest's theorem) for all one-particle properties, while remaining energy conserving for time-independent Hamiltonians. We present the time-dependent orbital-optimized coupled cluster doubles method (Keldysh-OCCD) in analogy with the formalism for zero-temperature dynamics, extended to finite temperatures through the time-dependent action on the Keldysh contour. To demonstrate the conservation property and understand the numerical performance of the method, we apply it to several problems of non-equilibrium finite-temperature dynamics: a 1D Hubbard model with a time-dependent Peierls phase, laser driving of molecular H$_2$, driven dynamics in warm-dense silicon, and transport in the single impurity Anderson model.