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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Theory

Background:

  • Dynamical Mean-Field Theory (DMFT) captures local correlations but neglects nonlocal effects.
  • Understanding phase transitions and critical behavior requires going beyond local approximations.

Purpose of the Study:

  • To develop a theoretical framework that systematically includes nonlocal correlations beyond DMFT.
  • To investigate the suppression of critical temperature and evolution of critical behavior.
  • To accurately predict the Néel temperature for the three-dimensional cubic Hubbard model.

Main Methods:

  • Variational perturbation expansion around DMFT.
  • Identification of symmetry breaking in paramagnetic diagrammatic expansions.
  • Introduction of a variational order parameter.

Main Results:

  • Accurate prediction of the Néel temperature across all interaction strengths with low computational cost.
  • Demonstration of significant modifications to magnetization and susceptibility in the intermediate correlation regime.
  • Establishment of Heisenberg critical behavior emerging beyond DMFT's mean-field description.

Conclusions:

  • The developed method systematically incorporates nonlocal correlations, improving upon DMFT.
  • The study accurately captures the transition from mean-field to Heisenberg universality classes near phase transitions.
  • This approach provides a computationally efficient and accurate tool for studying strongly correlated electron systems.