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Related Experiment Video

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Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Solving the parquet equations for the Hubbard model beyond weak coupling.

Ka-Ming Tam¹, H Fotso, S-X Yang

¹Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 16, 2013

Summary

Imposing crossing symmetry in the Hubbard model

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Area of Science:

Condensed matter physics
Quantum mechanics
Computational physics

Background:

The Hubbard model is a fundamental model in condensed matter physics for studying strongly correlated electron systems.
Solving the parquet equations for the Hubbard model is computationally challenging, especially at low temperatures and strong interactions.
Existing iterative methods often exhibit limited convergence ranges.

Purpose of the Study:

To extend the convergence range of solutions for the parquet equations in the Hubbard model.
To improve the efficiency and stability of iterative methods for solving correlated electron models.
To facilitate the solution of two-particle field theories for these models.

Main Methods:

Modification of the iterative algorithm to incorporate crossing symmetry.
Implementation of a latency hiding scheme for computational performance enhancement.
Inclusion of time reversal and point group symmetries (though found to not further improve convergence).

Main Results:

Imposing crossing symmetry significantly broadens the convergence range of the parquet equations.
Stable solutions are obtained more rapidly, even for strong interactions and low temperatures.
The modified algorithm achieves convergence where previous methods failed.

Conclusions:

Crossing symmetry is crucial for extending the convergence of iterative solutions to the Hubbard model's parquet equations.
The developed computational techniques offer a more efficient pathway to solving complex correlated electron models.
This work represents a significant advancement towards solving two-particle field theories for these systems.