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Dirac's method for constraints: an application to quantum wires.

¹Department of Physics, City College of the City University of New York, New York, NY 10031, USA.

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

|April 5, 2011

Summary

This summary is machine-generated.

We studied the infinite U Hubbard model, equivalent to preventing double occupancy. Our method revealed how constraints modify quantum commutators, explaining the 0.7 anomalous conductance in quantum wires.

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Area of Science:

Condensed Matter Physics
Quantum Mechanics
Statistical Mechanics

Background:

The Hubbard model is crucial for understanding strongly correlated electron systems.
The limit U = ∞ enforces the exclusion of double occupancy, a key constraint in certain physical systems.
Understanding quantum wires at finite temperatures is vital for nanoscale electronics.

Purpose of the Study:

To investigate the Hubbard model in the U = ∞ limit using Dirac's constraint method.
To analyze the impact of these constraints on the anomalous commutator.
To apply the developed theory to quantum wires and explain observed phenomena.

Main Methods:

Solving the Hubbard model in the U = ∞ limit via Dirac's method for constraints.
Utilizing the bosonization method to handle the constraints.
Applying the theoretical framework to quantum wires at finite temperatures.

Main Results:

The constraints were found to modify the anomalous commutator.
This modification was directly linked to the emergence of anomalous conductance.
A specific value of 0.7 for the anomalous conductance was predicted and explained.

Conclusions:

The study successfully explains the 0.7 anomalous conductance in quantum wires.
Dirac's constraint method combined with bosonization provides a powerful tool for analyzing the U = ∞ Hubbard model.
The findings offer insights into electron behavior in one-dimensional systems under strong correlation.