The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects
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Date
2021-07-13Author
Monacelli, Lorenzo
Bianco, Raffaello
Cherubini, Marco
Calandra, Matteo
Mauri, Francesco
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Journal of Physics: Condensed Matter 33 : (2021) // Article ID 363001
Abstract
[EN] The efficient and accurate calculation of how ionic quantum and thermal fluctuations impact
the free energy of a crystal, its atomic structure, and phonon spectrum is one of the main
challenges of solid state physics, especially when strong anharmonicy invalidates any
perturbative approach. To tackle this problem, we present the implementation on a modular
Python code of the stochastic self-consistent harmonic approximation (SSCHA) method. This
technique rigorously describes the full thermodynamics of crystals accounting for nuclear
quantum and thermal anharmonic fluctuations. The approach requires the evaluation of the
Born–Oppenheimer energy, as well as its derivatives with respect to ionic positions (forces)
and cell parameters (stress tensor) in supercells, which can be provided, for instance, by first
principles density-functional-theory codes. The method performs crystal geometry relaxation
on the quantum free energy landscape, optimizing the free energy with respect to all degrees of
freedom of the crystal structure. It can be used to determine the phase diagram of any crystal at
finite temperature. It enables the calculation of phase boundaries for both first-order and second-order phase transitions from the Hessian of the free energy. Finally, the code can also
compute the anharmonic phonon spectra, including the phonon linewidths, as well as phonon
spectral functions.We review the theoretical framework of the SSCHA and its dynamical
extension, making particular emphasis on the physical inter pretation of the variables present
in the theory that can enlighten the comparison with any other anharmonic theory. A modular
and flexible Python environment is used for the implementation, which allows for a clean
interaction with other packages.We briefly present a toy-model calculation to illustrate the
potential of the code. Several applications of the method in superconducting hydrides,
charge-density-wave materials, and thermoelectric compounds are also reviewed.
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