Fig. 6: Incompressible \({{\mathbb{Z}}}_{{\ell }_{{{{\rm{AB}}}}}}\) phases. | Communications Physics

Fig. 6: Incompressible \({{\mathbb{Z}}}_{{\ell }_{{{{\rm{AB}}}}}}\) phases.

From: Dynamical Aharonov-Bohm cages and tight meson confinement in a \({{\mathbb{Z}}}_{2}\)-loop gauge theory

Fig. 6

In a we plot the filling fraction ν at h/t = 0.05, for a chain of L = 120 sites. At small values of the electric field, quantum fluctuations of the flux restore the hopping among separate partitions. Nevertheless, regions of fixed filling fraction ν and flux are stabilized at ν = 0, \(\frac{1}{2}\), \(\frac{2}{3}\) and 1, corresponding to incompressible phases in which the chain is fully partitioned into single empty sites, fourmers, trimers and dimers respectively, as indicated by the labels inside each area that correspond to the average size of the Aharonov-Bohm cages ℓAB. As a result, the lattice translational symmetry is broken to the \({{\mathbb{Z}}}_{{\ell }_{{{{\rm{AB}}}}}}\) subgroup. In b we show the compressibility \(\kappa =\frac{\partial N}{\partial \mu }{| }_{J}\), demonstrating that the caged regions are incompressible areas of fixed filling ν, as indicated by the red labels in each lobe, and are separated by lines of diverging κ, at which the filling fraction changes abruptly.

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