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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
Infrared behavior in systems with a broken continuous symmetry: classical O(N) model versus interacting bosons
1Laboratoire de Physique Théorique de la Matière Condensée, CNRS-UMR 7600, Université Pierre et Marie Curie, 4 Place Jussieu, F-75252 Paris Cedex 05, France.
Summary
Systems with broken continuous symmetry face infrared divergences. This study explores the transition to the Goldstone regime, finding similarities between O(N) models and interacting bosons.
Area of Science:
- Condensed matter physics
- Quantum field theory
Background:
- Spontaneously broken continuous symmetries lead to infrared divergences in perturbative expansions.
- Transverse and longitudinal fluctuations couple, causing issues at low energies.
Purpose of the Study:
- Investigate the crossover from the high-energy Gaussian regime to the low-energy Goldstone regime.
- Analyze the diverging longitudinal susceptibility and singular self-energy.
- Compare classical O(N) models with interacting bosons at zero temperature.
Main Methods:
- Perturbation theory
- Hydrodynamic approach (Popov's theory for bosons)
- Large-N limit
- Nonperturbative renormalization group
Main Results:
- Identified the Ginzburg momentum scale (pG) as the breakdown point for perturbation theory.
- Observed significant similarities between the classical O(N) model and interacting bosons in the weak-coupling limit.
- Demonstrated the breakdown of perturbation theory at low energies due to coupled fluctuations.
Conclusions:
- The study highlights the critical role of the Ginzburg momentum scale in understanding symmetry breaking.
- Despite differences in their actions, classical O(N) models and interacting bosons exhibit analogous behavior in specific limits.
- Provides a comprehensive analysis of infrared divergences in systems with broken continuous symmetries.
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