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Sandbox Physics

Q058 · HOW CHANGE TRAVELS

Quantum Spin Chain Quench

Choose one spin, switch on neighboring interactions, and scrub through time. Compare the perturbed chain with an unflipped control, then collect complete spin snapshots.

Interactive modelQuantum Spin Chain Quench
Recorded shots00
Reference / current setting—\text{—}
PREPARE → SWITCH ON → EVOLVE—\text{—}

Drive after preparation

CouplingTransverse field

Unflipped control · same drive

Up expectationDown expectation

Arrows show local mean spin, not a trajectory or a single shot. Click a site to change the initial flip.

Sampling uses a fresh chain at the selected time. Scrubbing time starts a new record.

Ready. No measurements yet.

02 / WHAT WAS ACTUALLY RECORDED

One row, one complete chain.

Recorded magnetizationLatest full snapshotDashed: model reference

Site averages with one-standard-error bars. A single snapshot contains one up/down outcome per site.

M=0M=0

03 / SEPARATE CORRELATION FROM INFLUENCE

Correlated does not mean directly disturbed.

Connected correlation from recorded snapshots

Pure-state model reference · not a snapshot estimate

—\text{—}

Correlations are plug-in estimates from joint outcomes; no confidence interval is claimed for them. The diagonal is excluded. The time map and entropy curve are computed directly from the model.

Keep the evidence

Latest twelve shots shown; CSV retains all outcomes and settings. Save up to six samples and restore their exact settings and records.

Model, limits & scientific sources

Open nearest-neighbor chain; prepare all spins up, optionally flip one. Initial coupling is zero. Coupling and field reach their selected final values either immediately or through a linear ramp. Spins are not continuously measured during evolution. Finite chains recur; displayed smooth curves do not establish a thermodynamic phase transition.

Calabrese, Essler & Fagotti · 2012Jurcevic et al. · 2014

The ion experiment uses long-range interactions. It motivates the propagation question; this nearest-neighbor model does not reproduce that apparatus or its data.

—\text{—}

Physics tutorial

Quantum Spin Chain Quench

BackgroundChoose one spin, switch on neighboring interactions, and scrub through time. Compare the perturbed chain with an unflipped control, then collect complete spin snapshots.

Why it mattersChange one physical ingredient and keep a matched control.

Start with the essentials

Focus question
Flip one spin. Where does its influence go?
One-sentence intuition
A global quench can create correlations even without a local flip. Compare with the unflipped control to isolate the influence of that flip.

Core mathematical model

The specified chain

H(t)=−J(t)∑j=1L−1XjXj+1−h(t)∑j=1LZjH(t)=-J(t)\sum_{j=1}^{L-1}X_jX_{j+1}-h(t)\sum_{j=1}^L Z_j

Open boundaries. Time is in units of reduced Planck constant divided by the reference energy. The field points along the spin readout axis; the Ising coupling is transverse to it.

Connected correlation

Cij=⟨ZiZj⟩−⟨Zi⟩⟨Zj⟩C_{ij}=\langle Z_iZ_j\rangle-\langle Z_i\rangle\langle Z_j\rangle

Estimate both factors from the same joint spin snapshots. Nonzero correlations are not by themselves a measure of the influence of an initial local flip.

Half-chain entropy

SA=−Tr⁡(ρAlog⁡2ρA)S_A=-\operatorname{Tr}(\rho_A\log_2\rho_A)

Trace out the right half of the pure state. This is a model diagnostic, not a reconstruction from one measurement basis.

Common difficulties

What comes from the records?

Typical misconceptionEvery plotted quantity was measured.

Better mental modelRecorded magnetization and correlations come from joint snapshots. Time maps and entropy come from direct state evolution.

Scope

Typical misconceptionA small ideal model certifies a laboratory advantage.

Better mental modelAn isolated open chain of 4–8 spins with nearest-neighbor Ising interactions and a transverse field. Unitary evolution uses a converged time step. Entanglement entropy is a model reference, not inferred from the recorded spin snapshots. No thermodynamic transition or speed-of-light claim is made.

Run the experiment

  1. 01

    Predict

    Disconnect the neighbors and flip one spin.

    What to observe: No influence reaches the other sites.
  2. 02

    Operate and record

    Reconnect the chain. Play, pause, and collect snapshots at two times. Save each sample.

    What to observe: The local difference and connected correlations evolve differently.
  3. 03

    Break an assumption

    Switch on slowly, then change the chain length and inspect late times.

    What to observe: Preparation protocol and finite boundaries alter the result.