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Polaronic discontinuities induced by off-diagonal coupling.
Yuyu Zhang1, Liwei Duan, Qinghu Chen
1Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore.
The Journal of Chemical Physics
|July 27, 2012
Summary
Investigating the Holstein molecular crystal model reveals discontinuities in polaron energy and quantum entanglement for antisymmetric coupling. Symmetric coupling, however, shows a smooth transition in these properties.
Area of Science:
- Condensed Matter Physics
- Materials Science
- Quantum Mechanics
Background:
- The Holstein molecular crystal model describes the interaction between electronic excitations and lattice vibrations.
- Off-diagonal coupling, representing the influence of lattice vibrations on excitation transfer, is crucial for understanding material properties.
- Previous studies have explored various aspects of the Holstein model, but the impact of different off-diagonal coupling types on ground-state properties requires further investigation.
Purpose of the Study:
- To analyze the Holstein molecular crystal model with both symmetric and antisymmetric off-diagonal couplings.
- To investigate analyticity issues in the ground state properties, including polaron energy, phonon cloud size, and quantum entanglement.
- To examine the behavior of these properties in finite-sized lattices and the thermodynamic limit.
Main Methods:
- Application of the Toyozawa Ansatz.
- Utilizing the Lanczos algorithm for numerical diagonalization.
- Analysis of ground-state properties such as polaron energy dispersion, phonon cloud size, and linearized von Neumann entropy.
Main Results:
- For finite lattices with antisymmetric coupling, discontinuities were observed in polaron energy dispersion, phonon cloud size, and quantum entanglement.
- Antisymmetric coupling also led to a shift in ground-state crystal momentum from zero to non-zero values.
- In the thermodynamic limit, these discontinuities vanished except for the initial departure of the ground-state wavevector from the Brillouin zone center. Symmetric coupling resulted in smooth crossovers for all parameters.
Conclusions:
- Antisymmetric off-diagonal coupling introduces significant discontinuities in ground-state properties of the Holstein model, particularly in finite systems.
- The behavior of the ground-state wavevector is a robust indicator of these transitions, even in the thermodynamic limit.
- Symmetric off-diagonal coupling provides a more stable and continuous behavior, suggesting different physical implications for materials exhibiting these coupling types.
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