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The inclusion of temperature effects is important to properly simulate andinterpret experimentally observed vibrationally resolved electronic spectra. Wepresent a numerically exact approach for evaluating these spectra at finitetemperature using the thermofield coherence dynamics. In this method, whichavoids implementing an algorithm for solving the von Neumann equation for thecoherence, the thermal vibrational ensemble is first mapped to a pure-statewavepacket in an augmented space, and this wavepacket is then propagated bysolving the standard, zero-temperature Schr\"{o}dinger equation with thesplit-operator Fourier method. We show that the finite-temperature spectraobtained with the thermofield coherence dynamics in a Morse potential agreeexactly with those computed by Boltzmann-averaging the spectra of individualvibrational levels. Because the split-operator thermofield dynamics on a fulltensor-product grid is restricted to low-dimensional systems, we brieflydiscuss how the accessible dimensionality can be increased by varioustechniques developed for the zero-temperature split-operator Fourier method.

Finite-temperature vibronic spectra from the split-operator thermofield coherence dynamics