---
title: "Electric Strings and Screening Interactive Lab | Sandbox Physics"
description: "How can a dynamical particle pair weaken an electric string? A particle pair can screen the fixed charges and lower the electric-field energy."
canonical_url: "https://sandboxphysics.com/labs/string-breaking/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/string-breaking/"
---

FR04-B · A string can create its own screen

# Electric Strings and Screening

**How can a dynamical particle pair weaken an electric string?** A particle pair can screen the fixed charges and lower the electric-field energy. Creating the pair costs mass energy, so light matter responds more strongly. On a small isolated chain, screening and electric flux can oscillate and return.

Release an electric string between fixed charges and follow its quantum evolution. Compare light and heavy matter, move the right-hand source, and watch the electric field and particle density together.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

A finite, open, one-dimensional U(1) rotor Hamiltonian evolves staggered fermions in an exactly selected Gauss sector. Integer electric flux is truncated; the finite chain can revive. Colored links show electric-field expectations and spheres show matter-charge expectations, not individual particle tracks. The record is a deterministic model calculation, not QCD or experimental data.

Deterministic model calculation

## Electric field and matter respond together

Numerical diagnostics and full record

$\lVert\psi\rVert^2=1$

$C_{1,N-2}=\langle Q_1Q_{N-2}\rangle-\langle Q_1\rangle\langle Q_{N-2}\rangle$ is the connected charge correlation between site one and the second-to-last chain site. It uses the same wavefunction as the scene. The chain length determines these sites; moving an external source leaves them fixed.

The record saves the frozen Hamiltonian parameters, initial state, sampled numerical trajectory and conservation diagnostics. Curves join exact finite-matrix samples; all data are simulated.

The edge probability measures weight on states that touch the electric cutoff. It does not bound the truncation error; compare both cutoffs and the observables directly.

The Four-ion model reference uses the source-free ideal four-site Hamiltonian of Martinez et al. (2016), arXiv:1605.04570v1, Figure 2a. This is a numerical model reference; experimental points and hardware errors are excluded.

[Continue the course: Gauss law, strings and gauge protection](https://sandboxphysics.com/stories/lattice-gauge/)

Physics tutorial

## Electric Strings and Screening

**Background** Two fixed external charges initially hold an electric string across a staggered product state. Matter can hop, but every hop also changes an electric link.

**Why it matters** The field stores energy. If matter responds, some of that energy can accompany particle-pair excitations and screen the external sources.

Start with the essentials

- **Focus question**: How can a dynamical particle pair weaken an electric string?
- **One-sentence intuition**: Screening couples a change of charge density to a change of electric flux through Gauss law.

### Core mathematical model

#### The finite rotor Hamiltonian

$$
H=-w\sum_n(c_n^\dagger U_nc_{n+1}+\mathrm{h.c.})+m\sum_n(-1)^nN_n+\frac{g^2}{2}\sum_nE_n^2
$$

The three terms move matter with its link, set the staggered mass cost, and store electric energy. The link operator raises an integer flux by one; at the chosen electric cutoff its forbidden action is zero.

#### Counting bare particle pairs

$$
N_{\rm pair}=\sum_{n\;\mathrm{even}}\langle N_n\rangle
$$

At fixed half filling, each occupied even site has a matching hole on the odd sublattice. This counts excitations relative to the initial product state. A separate no-source product-state quench shows that some pairs also occur without external charges.

#### Evolution inside the physical sector

$$
|\psi(t)\rangle=e^{-iHt}|\psi(0)\rangle,\qquad G_n|\psi(t)\rangle=0
$$

The browser diagonalizes the small Hamiltonian and samples its exact finite-matrix evolution. Units set lattice spacing and the reduced Planck constant to one. A finite chain can return close to its starting state.

### Common difficulties

#### An expectation is not a particle track

**Typical misconception** The growing sphere shows one particle moving continuously through the chain.

**Better mental model** Each sphere shows the expected local matter charge of a superposition. A single measurement has discrete occupations; the plotted expectation averages their probabilities.

### Run the experiment

1. 01

   #### Follow field and matter together

   Watch Light matter screens, then pause and scrub Observation time through the first oscillation.

   **What to observe:** As matter charges develop near the external sources, central links dim. The field can grow again as the finite system evolves coherently.

2. 02

   #### Increase the mass

   Compare Heavy matter resists with the light-matter preset. Keep the electric coupling fixed when making your own comparison.

   **What to observe:** A larger mass increases the cost of particle-pair excitation. The string retains more of its original field for the selected settings.

3. 03

   #### Check the finite calculation

   Open Chain size and electric cutoff. Compare both cutoffs and save each trajectory; then try A longer string.

   **What to observe:** Differences measure sensitivity to the finite model. A late return on one short chain is a finite-volume feature; the exported norm, energy and Gauss diagnostics check numerical evolution.

Physical conclusion

Read field and charge together, and compare finite cutoffs before interpreting a string’s motion.

## Related experiments and articles

Lattice gauge fields and string breaking · Reading path

### Gauss constraints, screening and numerical control

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **The energy cost of stretching an electric-flux string**](https://sandboxphysics.com/stories/lattice-gauge/flux-energy/)
2. [Article **Following a released electric-flux string in time**](https://sandboxphysics.com/stories/lattice-gauge/string-dynamics/)
3. [Article **What electric cutoffs and short chains change**](https://sandboxphysics.com/stories/lattice-gauge/cutoff-finite-size/)
4. [Article **Independently recalculating a four-site pair-production curve**](https://sandboxphysics.com/stories/lattice-gauge/reproducible-comparison/)

Quantum & fields · Starter path

## Start from a single measurement

Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference.

[Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/)

1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/)
2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/)
3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/)
4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/)
5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/)
6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/)

[View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)