Skip to main content
Sandbox Physics

Q058 · Follow the effect of one flip

Quantum Spin Chain Quench

If you flip one spin in a chain, where does its influence go? The difference from an unflipped control spreads through neighboring couplings. A global quench also creates correlations, so comparing the two preparations isolates the influence of the initial flip.

Choose a site to flip and compare its chain with an unflipped control. Watch the mean spins evolve, then save joint snapshots at one observation time.

Interactive modelQuantum Spin Chain Quench
Live model time1.20 ℏ/E01.20\,\hbar/E_0
Frozen sample time1.20 ℏ/E01.20\,\hbar/E_0
Recorded chains200200
Largest change from control0.5830.583

Keep one measurement time fixed

A seeded sample is loaded on entry.

Frozen observation time: t=1.20 ℏ/E0t=1.20\,\hbar/E_0

Up readoutDown readoutWhite dashes: model at the saved time

Rows are independent chains; whiskers show one standard error.

Compare a local flip with a global quench

PositiveNegativeGold line: live timeViolet line: saved time

More shots and saved-time correlations

Each row is one simultaneous readout of an independently prepared chain. The mean and its standard error use all recorded chains at this single time.

Additional shots use the saved settings and saved observation time, even while the live scene moves. A new acquisition replaces the current sample; saved samples remain available for replay.

Correlation estimates use the joint outcomes and exclude the reference site itself. No confidence interval is assigned to these plug-in estimates.

Model, units and scientific sources

The model is an isolated open chain of four to eight spins with nearest-neighbor Ising coupling and a transverse field. Arrow lengths show local mean readouts; the saved sample stays at its labeled observation time.

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

Four to eight spin-half sites have open ends. Readouts are Pauli eigenvalues along the field direction; arrow lengths show their local expectations. Time is measured in the reduced Planck constant divided by the reference energy, and site spacing defines one length unit.

Every preparation starts with all sites up along the readout axis, with an optional local flip. Neighbor coupling starts at zero; a sudden switch or linear ramp sets the final drive. Midpoint Strang splitting evolves the full state vector with maximum step 0.005; step halving and independent finite-chain references check the numerical approximation.

Cij=⟨ZiZj⟩−⟨Zi⟩⟨Zj⟩,SA=−Tr⁡(ρAlog⁡2ρA)C_{ij}=\langle Z_iZ_j\rangle-\langle Z_i\rangle\langle Z_j\rangle,\qquad S_A=-\operatorname{Tr}(\rho_A\log_2\rho_A)

The time map and entropy are state-vector model references. Single-basis snapshots provide the displayed magnetization and correlation estimates. Finite chains recur; the picture does not establish a thermodynamic transition or a relativistic propagation speed.

SA=1.22 bitS_A=1.22\,\mathrm{bit}Δt≤0.005 ℏ/E0\Delta t\le0.005\,\hbar/E_0

Calabrese, Essler & Fagotti · 2012 · Eq. 1 and section 1.1

That paper studies a periodic chain prepared in a ground state. Here the open finite chain starts in a specified product state; the shared Ising Hamiltonian motivates the comparison, and the paper’s asymptotic formulas are not used as this sample’s measurement data.

Physics tutorial

A local disturbance and the correlations created by a global quench

BackgroundNeighboring spins interact after a coupling is switched on. One preparation has a single flipped spin; the control has no flip and follows the same drive.

Why it mattersA correlation between two spins can grow in both preparations. Comparing them tells us which change came from the local intervention.

Start with the essentials

Focus question
Which sites change because of the initial flip?
One-sentence intuition
The difference from the unflipped control measures the effect of the flip; connected correlation measures a different feature of the quantum state.

Core mathematical model

Open-chain transverse-field Ising Hamiltonian

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

The neighbor coupling acts along one spin axis and the field along the perpendicular readout axis. Both preparations start as specified product states. The full state vector is evolved by midpoint Strang splitting, with a maximum time step of 0.005 in the displayed time unit.

Change caused by the local preparation

Δj(t)=⟨Zj(t)⟩flip−⟨Zj(t)⟩control\Delta_j(t)=\langle Z_j(t)\rangle_{\mathrm{flip}}-\langle Z_j(t)\rangle_{\mathrm{control}}

The drive, chain length and observation time are the same in the two model calculations. Their difference isolates the effect of the one changed initial spin.

Connected correlation at one observation time

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

Joint outcomes supply both terms in a sampled estimate. The displayed correlation estimate uses one frozen observation time; records from different times are kept separate.

Common difficulties

An arrow is an average

Typical misconceptionEach arrow traces a spin following a definite path.

Better mental modelThe arrow shows the mean readout component of the local quantum state. A single joint snapshot instead contains an up or down outcome at every site.

Correlation and influence differ

Typical misconceptionAny new correlation must have come from the flipped spin.

Better mental modelSwitching the entire chain can create correlations even when no spin is flipped. Compare the locally changed preparation with its matched control.

A saved time stays fixed

Typical misconceptionLetting the scene play adds measurements from each new time to the same mean.

Better mental modelThe saved record keeps its own preparation, observation time and seed. Additional shots use those saved settings. “Record the live time” starts a new sample from the currently displayed state.

Run the experiment

  1. 01

    Find how a change spreads

    Choose “A local disturbance travels”, then drag the gold ring to a different site.

    What to observe: The two chains start differently at that site. Their model difference subsequently develops at neighboring sites.
  2. 02

    Separate a global quench

    Choose “Quench without a local flip” and view “Connected correlation”.

    What to observe: The two mean-spin chains agree, but connected correlations can still grow. The drive changed the whole chain.
  3. 03

    Freeze one measurement time

    Pause, choose a time and select “Record the live time”. Save that sample, move the live time, then replay the saved sample.

    What to observe: The replay restores the original parameters and raw shots without resampling. The shot chart is compared with the model at the record’s own observation time.
  4. 04

    Test the role of interaction

    Choose “Disconnected neighbors”, then compare with “Switch on gradually”.

    What to observe: Without neighbor coupling the flip affects only its original site. A gradual switch changes the driving history and the resulting spreading pattern.

Related experiments and articles

Condensed matter · Reading path

Magnetism, disorder and topological response

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

  1. ArticleHow atomic magnets can order and still cancel
  2. LabGMR Spin ValveGMR spin valve
  3. ArticleWhy apparently nonmagnetic states still respond to a field
  4. ArticleWhy integer and half-integer spin chains behave differently
  5. LabChern Insulator · Follow the EdgeChern insulator

Condensed matter · Reading path

Cold liquids and superconducting order

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

  1. ArticleWhat nuclear resonance revealed about pairing in helium-three
  2. LabBEC–BCS CrossoverPairing across the crossover

Fields, scales and critical phenomena · Reading path

From field modes to critical phenomena

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

  1. ArticleWhat a correlation function predicts
  2. LabEuclidean Field Correlations
1 more group

Conformal bootstrap · Reading path

From a critical chain to the kink in the 2D bound

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

  1. ArticleWhy a critical chain looks the same at every scale
  2. LabQuantum Critical Ising Chain: The Same Pattern at Every ScaleCollapse the rings
FeedbackSomething broken, confusing, or missing on this page?Tell us
What kind of feedback?

Sent with this page’s address, its Lab ID, the site language and your device type. Please leave out personal details. Feedback is kept for up to 12 months.Privacy policy