Dynamical Aharonov-Bohm cages and tight meson confinement in a Z2-loop gauge theory
Abstract
We study the finite-density phases of a Z2 lattice gauge theory (LGT) of interconnected loops and dynamical Z2 charges. The gauge-invariant Wilson terms, accounting for the magnetic flux threading each loop, correspond to simple two-body Ising interactions in this setting. Such terms control the interference of charges tunneling around the loops, leading to dynamical Aharonov-Bohm (AB) cages that are delimited by loops threaded by a π-flux. The latter can be understood as Z2 vortices, the analog of visons in two dimensional LGTs, which become mobile by adding quantum fluctuations through an external electric field. In contrast to a semi-classical regime of static and homogeneous AB cages, the mobile visons can self-assemble leading to AB cages of different lengths depending on the density of Z2 charges and the interplay of magnetic and electric terms. Inside these cages, the individual charges get confined into tightly-bound charge-neutral pairs, the Z2 analogue of mesons. Depending on the region of parameter space, these tightly-bound mesons can propagate within dilute AB-dimers that virtually expand and contract, or else move by virtually stretching and compressing an electric field string. Both limits lead to a Luttinger liquid described by a constrained integrable model. This phase is separated from an incompressible Mott insulator where mesons belong to closely-packed AB-trimers. In light of recent trapped-ion experiments for a single Z2 loop, these phases could be explored in future experiments.
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