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

Abstract Low-dimensional lattice gauge theories based on simplified gauge groups have emerged as relevant models of charge-confinement that can potentially be realized with quantum simulators. The intertwined dynamics of matter and gauge fields can result in quantum phases of the confined matter that have not yet been fully explored, especially in connection to the underlying mechanisms behind confinement. Here we study the finite-density phases of a $${{\mathbb{Z}}}_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> lattice gauge theory of interconnected loops and dynamical $${{\mathbb{Z}}}_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> charges. We show that the gauge-magnetic flux threading each loop is responsible for a phenomenon of dynamical Aharonov-Bohm caging, determining the confinement of particles into tightly-bound charge-neutral pairs, the $${{\mathbb{Z}}}_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> analogue of mesons. The latter are trapped inside the cages, which become mobile by adding quantum fluctuations through an external electric field. These tightly-bound mesons can either propagate, manifesting a Luttinger liquid behaviour, or form an incompressible Mott insulator. In light of recent trapped-ion experiments for a single $${{\mathbb{Z}}}_{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> loop, these phases could be explored in future experiments.