Dynamical Aharonov-Bohm cages and tight meson confinement in a $\mathbb{Z}_2$-loop gauge theory

• URL: http://arxiv.org/abs/2412.12425v1
• Date: Tue, 17 Dec 2024 00:26:24 GMT
• Title: Dynamical Aharonov-Bohm cages and tight meson confinement in a $\mathbb{Z}_2$-loop gauge theory
• Authors: Enrico C. Domanti, Alejandro Bermudez, Luigi Amico,
• Abstract summary: We study the finite-density phases of a $mathbbZ$ lattice gauge theory (LGT) of interconnected loops and dynamical $mathbbZ$ charges.
• Score: 44.99833362998488
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the finite-density phases of a $\mathbb{Z}_2$ lattice gauge theory (LGT) of interconnected loops and dynamical $\mathbb{Z}_2$ 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 $\pi$-flux. The latter can be understood as $\mathbb{Z}_2$ 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 $\mathbb{Z}_2$ charges and the interplay of magnetic and electric terms. Inside these cages, the individual charges get confined into tightly-bound charge-neutral pairs, the $\mathbb{Z}_2$ 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 $\mathbb{Z}_2$ loop, these phases could be explored in future experiments.

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