Lattice gauge theories (LGTs) provide valuable insights into problems in strongly correlated many-body systems. Confinement which arises when matter is coupled to gauge fields is just one of the open problems, where LGT formalism can explain the underlying mechanism. However, coupling gauge fields to dynamical charges complicates the theoretical and experimental treatment of the problem. Developing a simplified mean-field theory is thus one of the ways to gain new insights into these complicated systems. Here we develop a mean-field theory of a paradigmatic 1+1D \mathbb{Z}_2 ℤ 2 lattice gauge theory with superconducting pairing term, the gauged Kitaev chain, by decoupling charge and \mathbb{Z}_2 ℤ 2 fields while enforcing the Gauss law on the mean-field level. We first determine the phase diagram of the original model in the context of confinement, which allows us to identify the symmetry-protected topological transition in the Kitaev chain as a confinement transition. We then compute the phase diagram of the effective mean-field theory, which correctly captures the main features of the original LGT. This is furthermore confirmed by the Green’s function results and a direct comparison of the ground state energy. This simple LGT can be implemented in state-of-the art cold atom experiments. We thus also consider string-length histograms and the electric field polarization, which are easily accessible quantities in experimental setups and show that they reliably capture the various phases.
String breaking is an intriguing phenomenon crucial to the understanding of lattice gauge theories (LGTs), with strong relevance to both condensed matter and high-energy physics (HEP). Recent experiments investigating string breaking in
2+1D (two spatial and one temporal dimensions) LGTs motivate a thorough analysis of its underlying mechanisms. Here, we perform matrix product state (MPS) simulations of string breaking in an experimentally relevant
2+1D
Z2 LGT in the presence of two external charges. We provide a detailed description of the system in the confined phase, highlight a number of mechanisms which are responsible for string breaking, and argue that magnetic fluctuations have a stabilizing effect on the strings. Moreover, we show that deep in the confined regime the problem is dual to one-dimensional free fermions hopping on an open chain. Our work elucidates the microscopic processes of string breaking in
2+1D LGTs, and our findings can be probed on current superconducting-qubit quantum computers.