Functional-integral studies of correlated fermions
Abstract
Functional-integral techniques are used to study correlated fermion models of popular interest: the prototypical Hubbard models. Recent progress has been made in the functional-integral approach to such correlated Fermi systems by introducing a spin-space reference frame that :fluctuates in space and time, Introducing fermions with varying quantization a.xis on the lattice allows the functional-integral representation to assume a uniform approximation over the entire range of the interaction strength U, reproducing the expected mean fields at the saddlepoints along with gapless excitation spectrums. First, the framework necessary for this study is developed: second quantization and the second quantized models of correlated fermions that are to be examined are briefly reviewed. Next, an introduction to first and second quantized functional integrals is followed by basic functional-integral techniques employed to study quantum many-particle systems. Once the background necessary to investigate this approach has been given, the :fluctuating spin-space reference frame is described and is examined in the two-site problem, where an exact diagonalization may be performed. A functional-integral over one-vertex polygonal paths is used to approximate the partition function in a fixed reference frame orientation. This functional-integral representation is studied in the low-to-intermediate and high temperature regimes. A classification of the quantization a.xis configurations, based on classical spin waves, is motivated and presented.
Notes
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Thesis Completion
1993
Semester
Summer
Advisor
Johnson, Michael D.
Degree
Bachelor of Science (B.S.)
College
College of Arts and Sciences
Degree Program
Physics
Subjects
Arts and Sciences -- Dissertations, Academic;Dissertations, Academic -- Arts and Sciences
Format
Identifier
DP0020852
Language
English
Access Status
Open Access
Length of Campus-only Access
None
Document Type
Honors in the Major Thesis
Recommended Citation
De Lia, Anthony Francis, "Functional-integral studies of correlated fermions" (1993). HIM 1990-2015. 26.
https://stars.library.ucf.edu/honorstheses1990-2015/26