Non-commutative field theory approach to two-dimensional vortex liquid system
Kyungsun Moon, Vincent Pasquier, Chaiho Rim, and Joonhyun Yeo
TL;DR
This paper applies non-commutative field theory to model the vortex liquid system in the lowest Landau level, revealing a new gauge-invariant quartic potential and establishing its relation to traditional Ginzburg-Landau theory.
Contribution
It introduces a non-commutative field theory framework for vortex liquids and derives a novel gauge-invariant quartic potential, connecting it to existing Ginzburg-Landau models.
Findings
Non-commutative field theory effectively captures LLL physics.
A new gauge-invariant quartic potential is formulated.
The new interaction term is equivalent to traditional GL interactions.
Abstract
We investigate the non-commutative (NC) field theory approach to the vortex liquid system restricted to the lowest Landau level (LLL) approximation. NC field theory effectively takes care of the phase space reduction of the LLL physics in a -product form and introduces a new gauge invariant form of a quartic potential of the order parameter in the Ginzburg-Landau (GL) free energy. This new quartic interaction coupling term has a non-trivial equivalence relation with that obtained by Br\'ezin, Nelson and Thiaville in the usual GL framework. The consequence of the equivalence is discussed.
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