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A Green's function decoupling scheme for the Edwards fermion-boson model.

D M Edwards¹, S Ejima, A Alvermann

¹Department of Mathematics, Imperial College London, London SW7 2BZ, UK. d.edwards@imperial.ac.uk

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|March 16, 2011

Summary

This summary is machine-generated.

This study analytically calculates the one-particle Green's function for spinless fermions in a Mott insulator model. Results for the one-dimensional case agree with numerical methods, illuminating ground state properties at various densities.

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Setting Limits on Supersymmetry Using Simplified Models

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Published on: November 15, 2013

Area of Science:

Condensed Matter Physics
Quantum Mechanics
Materials Science

Background:

Mott insulators exhibit complex behavior with holes, modeled as spinless fermions interacting with bosons.
Previous studies primarily used numerical methods like Density Matrix Renormalization Group (DMRG) for the one-dimensional (1D) case at half-filling.

Purpose of the Study:

To analytically calculate the one-particle Green's function for the fermion-boson model across arbitrary densities in 1D, 2D, and 3D.
To compute ground state properties and the one-fermion spectral function using the derived Green's function.
To validate the analytical approach by comparing results with established numerical methods.

Main Methods:

Analytical calculation of the one-particle Green's function using a decoupling scheme for equations of motion.
Application of the method for large boson energy and zero boson relaxation parameter.
Computation of ground state properties and spectral functions for specific fermion densities (n = 0.1, 0.5, 0.9) in 1D.

Main Results:

The analytical Green's function provides accurate ground state properties and spectral functions in the 1D case.
Results show good agreement with numerical data from DMRG and dynamical DMRG methods.
The study offers new insights into the nature of the ground state at different fermion densities.

Conclusions:

The decoupling scheme for the Green's function is a successful analytical tool for the fermion-boson model.
The method's efficacy in 1D supports its potential for extension to 2D and 3D systems.
This work advances the understanding of Mott insulator physics and provides a foundation for future theoretical investigations.