Thermofield theory for finite-temperature quantum chemistry

Abstract

Thermofield dynamics has proven to be a very useful theory in high-energy physics, particularly since it permits the treatment of both time-and temperature-dependence on an equal footing. We here show that it also has an excellent potential for studying thermal properties of electronic systems in physics and chemistry. We describe a general framework for constructing finite temperature correlated wave function methods typical of ground state methods. We then introduce two distinct approaches to the resulting imaginary time Schrödinger equation, which we refer to as fixed-reference and covariant methods. As an example, we derive the two corresponding versions of thermal configuration interaction theory, and apply them to the Hubbard model, while comparing with exact benchmark results.

Thermofield Theory for Finite-Temperature Coupled Cluster

“…We note, however, that this choice is different from the one used in Ref. 42, where we use simply the one-electron Hamiltonian to con-struct H 0 .…”

“…However, as we have discussed in Ref. 42, one can chose any value of chemical potential α 0 and temperature β 0 to construct the thermal reference state. It is merely a matter of comfort to use α 0 = 0 = β 0 as the corresponding initial conditions for the cluster amplitudes are trivial.…”

“…In this paper, we present an alternative approach to thermal coupled cluster based on the thermofield dynamics (TFD), [38][39][40][41] using a framework we recently explored in Ref. 42. Thermofield dynamics provides a convenient way to represent the thermal density matrix via a wavefunction which evolves in temperature according to the imaginary-time evolution Schrödinger equation.…”

Finite-temperature coupled cluster: Efficient implementation and application to prototypical systems

“…45 The goal is to develop hierarchies that mirror those at zero temperature and approach the thermal full configuration interaction (FCI) 46 limit with polynomial scaling approaches. Examples include finite temperature extensions of perturbation theory, 47,48 configuration interaction (CI), 49 Green's function methods, [50][51][52] or coupled cluster (CC) theory. 47,[53][54][55][56] The coupled cluster method is the method of choice for high-accuracy, ground-state, quantum chemistry calculations, [57][58][59][60][61][62][63] and we believe it to be a promising arXiv:2004.01729v1 [physics.chem-ph] 3 Apr 2020 method for finite temperature calculations as well.…”

Real-time density-matrix coupled-cluster approach for closed and open systems at finite temperature

“…The subscript "c" in Eq. (27) denotes that only the connected part of the expression in the brackets has to be considered as a result of the cancellation of the disconnected part by the nested commutators. To derive differential equations for the cluster amplitudes, we project Eq.…”