Gauging spin

M. C. Aronson

Gautam Goswami, Pratul Bandyopadhyay

The gauge theoretical formulation of a spin system is studied here. It is pointed out that a quantum spin can be associated with a gauge bundle where the gauge group is SU(2). The Ising spin is obtained by breaking the group to U(1) coupled with a Z2 symmetry giving rise to a Z2 gauge theory in three dimension. The gauge structure of a spin system helps us to reformulate the block-variable transformation in terms of a gauge transformation.

D. Gershoni

Shi-Liang Zhu, Hao Fu, Congjun Wu +2 more

We propose an experimental scheme to observe spin Hall effects with cold atoms in a light-induced gauge potential. Under an appropriate configuration, the cold atoms moving in a spatially varying laser field experience an effective spin-dependent gauge potential. Through numerical simulation, we demonstrate that such a gauge field leads to observable spin Hall currents under realistic conditions. We also discuss the quantum spin Hall state in an optical lattice.

Stanley Gudder

Michael Pretko

Spin liquids are conventionally described by gauge theories with a vector gauge field. However, there exists a wider class of spin liquids with higher rank tensors as the gauge variable. In this work, we focus on (3+1)-dimensional spin liquids described by U(1) symmetric tensor gauge theories, which have recently been shown to be stable gapless spin liquids. We investigate the particle structure of these tensor gauge theories and find that they have deep connections with the “fracton” models recently discovered by Vijay, Haah, and Fu. Tensor gauge theories have more conservation laws than the simple charge conservation law of rank 1 theories. These conservation laws place severe restrictions on the motion of particles. Particles in some models are fully immobile (fractons), while other models have particles restricted to motion along lower-dimensional subspaces.