Physicists have, for the first time, simulated how an electric flux string breaks in a lattice version of quantum electrodynamics (QED) with three spatial dimensions. A “string” here means the narrow tube of electric field that connects two fixed charges. When this string carries enough energy, it can turn that energy into pairs of particles and antiparticles that screen the charges and cut the string — a process known as string breaking.

The team used a classical computational method called tree tensor networks (TTNs) to follow the real-time evolution of a 3+1 dimensional U(1) lattice gauge theory with dynamical matter. Lattice gauge theory means the continuous space of QED is replaced by a discrete grid so the quantum fields live on sites and links. They represent the gauge field with a spin-based “quantum-link” regularization and place matter on the lattice using staggered fermions, then start the system out of equilibrium (a quench) and watch how the electric flux evolves. The authors checked that their results converge by comparing to exact diagonalization where possible and by varying the truncation of the gauge field.

At strong coupling they find a clear, resonant form of string breaking. When the particle mass and the gauge coupling meet a sharp resonance condition, electric energy turns into matter–antimatter pairs that screen the fixed charges and thus sever the string. Away from that resonance, the picture is noisier: many different processes compete with string breaking. These include pair production in many places, deformations and extensions of the string into transverse directions, and the creation of closed flux loops. Because the number of such competing channels grows with system size, they can drain away the original string sector even far from resonance.

The simulations also clarify which physical terms drive which effects. The hopping term in the Hamiltonian moves charges and can create dynamical particles that screen flux. The magnetic or “plaquette” term acts on small square faces of the lattice and makes the string bulge or form membrane-like deformations in transverse directions. The authors further develop a channel-resolved perturbation theory — a way to separate and track the different microscopic channels — and show it reproduces the observed dynamics and the frequency content (Fourier spectrum) of the evolution.