Dynamic Pseudogap Model: Analytic Results vs Monte Carlo Numerics
Abstract
Recently proposed dynamic pseudogap model analytical results for spectral density of an electron scattered by random time-dependent Gaussian field representing fluctuations with finite nesting vector bf Q, characteristic oscillation frequency ω0 and damping γ, leading to pseudogap formation, are compared with exact numerical solution by Monte Carlo (MC) approach. We consider both commensurate (real) and incommensurate (complex) fluctuations, for a wide range of parameters of the model. Electron Green's function is approximated either by a double Poisson series with history-dependent Bogoliubov gaps or by exact static continued fraction solution. In the coherent regime double-series representation provides description of dynamic sideband formation in the spectral density. As coherence is progressively lost, the theory crosses over to the quasistatic fluctuating-gap regime described by the exact continued-fraction solution. The exact MC solution overcomes the limitations of analytic approach, such as neglect of Magnus-type corrections in commuting approximation, and establish the limits of analytic approach, as well as confirming the exactness of continued fraction solution in static limit. In general, analytic expressions demonstrate rather satisfactory agreement with exact MC numerics within their limits, confirming the overall qualitative physical picture of dynamic pseudogap formation.
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BibTeX
@misc{sadovskii2026dynamic,
title = {{Dynamic Pseudogap Model: Analytic Results vs Monte Carlo Numerics}},
author = {Michael V. Sadovskii},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33436},
eprint = {2610.33436},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33436},
}
RIS
TY - UNPB
TI - Dynamic Pseudogap Model: Analytic Results vs Monte Carlo Numerics
AU - Michael V. Sadovskii
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33436
UR - https://arxiv.org/abs/2610.33436
AB - Recently proposed dynamic pseudogap model analytical results for spectral density of an electron scattered by random time-dependent Gaussian field representing fluctuations with finite nesting vector bf Q, characteristic oscillation frequency ω_0 and damping γ, leading to pseudogap formation, are compared with exact numerical solution by Monte Carlo (MC) approach. We consider both commensurate (real) and incommensurate (complex) fluctuations, for a wide range of parameters of the model. Electron Green's function is approximated either by a double Poisson series with history-dependent Bogoliubov gaps or by exact static continued fraction solution. In the coherent regime double-series representation provides description of dynamic sideband formation in the spectral density. As coherence is progressively lost, the theory crosses over to the quasistatic fluctuating-gap regime described by the exact continued-fraction solution. The exact MC solution overcomes the limitations of analytic approach, such as neglect of Magnus-type corrections in commuting approximation, and establish the limits of analytic approach, as well as confirming the exactness of continued fraction solution in static limit. In general, analytic expressions demonstrate rather satisfactory agreement with exact MC numerics within their limits, confirming the overall qualitative physical picture of dynamic pseudogap formation.
ER -