At the heart of quark confinement and hadronization, the physics of flux strings has recently become a focal point in the field of quantum simulation of high-energy physics (HEP). Despite considerable progress, a detailed understanding of the behavior of flux strings in quantum simulation-relevant lattice formulations of gauge theories has remained limited to the lowest truncations of the gauge field, which are severely limited in their ability to draw conclusions about the quantum field theory limit. Here, we employ tensor network simulations to investigate the behavior of flux strings in a quantum link formulation of $2+1$D quantum electrodynamics (QED) with a spin-$1$ representation of the gauge field. We first map out the ground-state phase diagram of this model in the presence of two spatially separated static charges, revealing distinct microscopic processes responsible for string breaking, including a two-stage breaking mechanism not possible in the spin-$\frac{1}{2}$ formulation. Starting in different initial product state string configurations, we then explore far-from-equilibrium quench dynamics across various parameter regimes, demonstrating genuine $2+1$D real-time string breaking and glueball-like bound state formation, with the latter not possible in the spin-$\frac{1}{2}$ formulation. In and out of equilibrium, we consider different values and placements of the static charges. Finally, we provide efficient qudit circuits for a quantum simulation experiment in which our results can be observed in state-of-the-art ion-trap setups. Our findings lay the groundwork for quantum simulations of flux strings towards the quantum field theory limit.
Umberto Borla, Jesse J. Osborne, Sergej Moroz
et al.
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 $2+1$D (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 $2+1$D $\mathbb{Z}_2$ 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 $2+1$D LGTs, and our findings can be probed on current superconducting-qubit quantum computers.
We study decomposition of $SU(2)$ gauge field into monopole and monopoleless components. After fixing the Maximal Abelian gauge in $SU(2)$ lattice gauge theory we decompose the nonabelian gauge field into the Abelian field created by monopoles and the modified nonabelian field with monopoles removed. We then calculate respective static potentialis and show that the potential due to the modified nonabelian field is nonconfining while, as is well known, the Abelian field produces linear potential. We further find that the sum of these potentials approximates the nonabelian static potential with good precision at all distances considered. We conclude that at large distances the monopole field potential describes the classical energy of the hadronic string while the static potential due to the modified nonabelian field describes the string fluctuations energy.