Conservation laws in coupled cluster dynamics at finite temperature

Abstract

We extend the finite-temperature Keldysh non-equilibrium coupled cluster theory (Keldysh-CC) [J. Chem. Theory Comput. 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 timedependent 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.

The normal state of attractive Fermi gases from coupled-cluster theory

“…This straightforward access to dynamical response functions should be contrasted with that of most QMC methods, which require analytic continuation. CC methods can also be applied to nonuniform systems, precluding the local density approximation for trapped gases, as well as at nonzero temperature [132][133][134][135][136][137] and in non-equilibrium settings [138][139][140]. Lastly and perhaps most importantly, CC theory can be formulated with respect to a BCS reference wavefunction, as opposed to the normal Fermi sea wavefunction used here, allowing a more accurate study of pairing and superfluidity [141][142][143][144][145][146].…”

Piecewise Interaction Picture Density Matrix Quantum Monte Carlo

“…Taken together, our results show that PIP-DMQMC is a promising development for DMQMC. Our long-term goal is to make DMQMC a resource for benchmarking finite temperature methods development [8][9][10][11][12][13][14][15][16][17][18][19][20][21] as well as describing electronic structure phenomena at finite temperature. With this in mind, two limitations of our study were that we did not systematically study convergence with initiator parameters or with starting initialization.…”

“…There has been a recent push to take methods which are effective for solving ground state electronic structure problems, especially quantum chemical wavefunction methods, and adapting them to treat finite temperature. Examples of this include perturbation theories [8][9][10][11][12] and coupled cluster techniques [13][14][15][16][17][18][19][20][21] . Other ab initio methods under active development include ft-DFT [22][23][24][25][26] and various flavors of Green's function methods [27][28][29][30][31][32][33] such as self-consistent second-order perturbation theory (GF2) and GW theory.…”

Time‐dependent coupled‐cluster theory

“…Up to this point all time‐dependence and temperature‐dependence was kept in the cluster amplitudes. However, in 2021 Peng et al 153 extended the Keldysh‐CC method to include orbital rotations. They formulated the Keldysh‐OCC method as an extension of the TDOCC method 85 to finite‐temperature systems.…”