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2018

Eliminating fermionic matter fields in lattice gauge theories

Zohar, Erez, Cirac, J. Ignacio

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We devise a unitary transformation that replaces the fermionic degrees of freedom of lattice gauge theories by (hard-core) bosonic ones.

The resulting theory is local and gauge invariant, with the same symmetry group.
The method works in any spatial dimensions and can be directly applied, among others, to the gauge groups $G=U(N)$ and $SU(2N)$, where $N\in\mathbb{N}$.
For $SU(2N+1)$ one can also carry out the transformation after introducing an extra idle $\mathbb{Z}_2$ gauge field, so that the resulting symmetry group trivially contains $\mathbb{Z}_2$ as a normal subgroup.

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S. P. Jordan, K. S. M. Lee, and J. Preskill, arXiv:1404.7115 [hep-th] (2014)

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Note that we build an analogy with the gauge transformation that takes place in that mechanism, and not about the symmetry breaking it is related to there

Cited in the paper.

E. A. Martinez, C. A. Muschik, P. Schindler, D. Nigg, A. Erhard, M. Heyl, P. Hauke, M. Dalmonte, T. Monz, P. Zoller, and R. Blatt, Nature 534

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S. Bravyi, J. Gambetta, A. Mezzacapo, and K. Temme, arXiv:1701.08213 [quant-ph] (2017)

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