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Enhanced electron-phonon coupling near an electronic quantum phase transition: Beyond the adiabatic approximation
Samuel Peter John Ladd1, Sachit Chavda1, Rosie Sibley1
1Department of Physics, Durham University, South Road, Durham, DH1 3LE, United Kingdom of Great Britain and Northern Ireland.
Summary
Electron-phonon coupling enhancement near quantum phase transitions is investigated. The study confirms that localized phonon states and mode hardening persist in the exact coupled electron-phonon problem, not just in approximations.
Area of Science:
- Condensed Matter Physics
- Quantum Phase Transitions
- Electron-Phonon Interactions
Background:
- Previous work predicted enhanced electron-phonon coupling near electronic quantum phase transitions using the Born-Oppenheimer approximation.
- This approximation suggested a potential energy barrier, localized phonon states, and phonon mode hardening.
- The survival of these effects in the exact coupled electron-phonon system remained an open question.
Purpose of the Study:
- To investigate whether the enhanced electron-phonon coupling, predicted by the Born-Oppenheimer approximation, is present in the exact coupled electron-phonon problem.
- To analyze the behavior of phonon modes and state localization in the exact theory across different electronic energy scales.
Main Methods:
- Direct diagonalization of the full coupled electron-phonon model.
- Analysis of the exact coupled electron-phonon excitation spectrum.
- Examination of the ground state using the parametric representation of the electron-nuclear wavefunction.
Main Results:
- The exact solution reproduces the adiabatic picture (including the Born-Oppenheimer correction) when electronic levels are well-separated.
- This picture is smoothed and weakened as electronic and phononic energy scales become comparable.
- In the near-degenerate regime, the exact solution transitions to a diabatic description.
Conclusions:
- The observed localization and phonon hardening are not artifacts of the Born-Oppenheimer approximation.
- These signatures survive in a renormalized form in the exact theory.
- The validity of the adiabatic picture depends on the separation of electronic energy levels.
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