Thermofield Theory for Finite-Temperature Electronic Structure.

Area of Science:

• Quantum Many-Body Physics
• Computational Chemistry
• Statistical Mechanics

Background:

• Wave function methods accurately approximate ground-state properties in quantum systems.
• Existing methods struggle to compute thermal properties due to the complexity of Hilbert space traces.
• Excited-state theories are less developed than ground-state theories.

Purpose of the Study:

• To present a finite-temperature wave function formalism overcoming limitations of existing methods.
• To generalize established ground-state wave function theories to finite temperatures.
• To enable accurate computation of thermal properties for quantum many-body systems.

Main Methods:

• Utilizing thermofield dynamics to map thermal density matrices to pure states in an expanded Hilbert space.
• Developing a procedure to generalize ground-state wave function theories (e.g., coupled cluster) to finite temperatures.
• Applying the formalism to Fermions in the grand-canonical ensemble and performing benchmark studies.

Main Results:

• Formulations of mean-field, configuration interaction, and coupled cluster theories for thermal properties are presented.
• Benchmark studies on the one-dimensional Hubbard model show thermal methods perform comparably to ground-state counterparts.
• The computational cost is shown to increase only by a prefactor.

Conclusions:

• The developed formalism provides a robust and systematically improvable approach to quantum thermal properties.
• The methods inherit the strengths and weaknesses of their ground-state analogues.
• This work opens avenues for future development in quantum thermal physics and computational methods.