Topological Quantum Phase Transition in Synthetic Non-Abelian Gauge Potential

TL;DR

This paper studies a topological quantum phase transition in Fermi gases on a honeycomb lattice influenced by synthetic non-Abelian gauge potentials, combining theoretical and numerical approaches to explore experimental detection methods.

Contribution

It develops a fermionic effective field theory for the topological transition and compares it with lattice numerical calculations, proposing new experimental detection techniques.

Findings

Effective field theory describes the topological transition.

Numerical results agree with theoretical predictions.

Proposed methods for experimental detection of the transition.

Abstract

The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non- Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and ex- plore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase tran- sition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops.