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Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions
Petar Mitrić1, Veljko Janković1, Nenad Vukmirović1
1Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia.
Dynamical mean field theory offers an excellent, cost-effective approximate solution for the Holstein model
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Theory
Background:
- The Holstein model describes electron-phonon interactions.
- Dynamical Mean Field Theory (DMFT) is typically limited to dimensions > 2 for this model.
Purpose of the Study:
- To evaluate DMFT as an approximate solution for the Holstein model across all parameter regimes, including one dimension.
- To compare DMFT results with numerically exact methods.
Main Methods:
- Dynamical Mean Field Theory (DMFT)
- Momentum-space numerically exact Hierarchical Equations of Motion (HEOM)
- Path Integral Quantum Monte Carlo (QMC)
- Exact Diagonalization (ED)
Main Results:
- DMFT provides an excellent and computationally inexpensive approximation for the Holstein model's spectral function, even in one dimension.
- Results show good agreement between DMFT and numerically exact methods (HEOM, QMC, ED).
Conclusions:
- DMFT is a viable and efficient approximate method for studying the Holstein model in various dimensions and coupling strengths.
- This broadens the applicability of DMFT in condensed matter physics research.
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