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Quantum Many-Body Scars
Why Some Initial States Refuse to Thermalise
Wait, What? A Non-Integrable Quantum System Can Forget Most Initial States but Remember a Few Special Ones
Generic isolated many-body quantum systems are expected to thermalise: after enough time, simple observables lose detailed memory of the initial state.
Yet certain strongly interacting systems contain exceptional initial states that undergo repeated coherent revivals instead of rapidly relaxing toward thermal values.
the system is not globally non-ergodic; a sparse special sector resists the thermal behaviour followed by most of the spectrum.
These atypical structures are called quantum many-body scars.
Quick Answer
Quantum many-body scars are special nonthermal eigenstates embedded inside an otherwise thermal spectrum. Certain simple initial states overlap strongly with this sparse scarred subspace, so their time evolution repeatedly rephases and returns unusually close to the starting state.
The phenomenon is called weak ergodicity breaking because most states still behave thermally. It differs from integrability, where an extensive set of conservation laws constrains the whole system, and from many-body localization, where disorder can prevent thermalisation for a broad set of states.
Nature Physics — Weak Ergodicity Breaking From Quantum Many-Body Scars →
Nature Physics Review — Quantum Many-Body Scars and Weak Breaking of Ergodicity →
What You Will Learn
- What thermalisation means in an isolated quantum system.
- What the eigenstate thermalization hypothesis predicts.
- Why most initial states lose detailed memory.
- What makes a scarred eigenstate atypical.
- How a tower of scarred states creates revivals.
- Why the Néel-like state in the Rydberg PXP model is special.
- Why scars are weak rather than global ergodicity breaking.
- How scars differ from integrability and many-body localization.
- Why low entanglement is useful evidence but not a universal definition.
- How experiments measure fidelity and local-observable revivals.
- How 2025–2026 work extends scar physics beyond the original model.
- Where the term “scar” becomes too broad or metaphorical.
Part 1 — The Naive Model: A Complex Quantum System Should Forget Its Start
Consider many interacting quantum degrees of freedom evolving under a time-independent Hamiltonian.
If the system is non-integrable and sufficiently complex, local observables often approach values predicted by statistical mechanics, even though the full wavefunction evolves unitarily and never truly loses information.
This apparent thermalisation is one of the central bridges between quantum mechanics and thermodynamics.
Part 2 — Eigenstate Thermalization Hypothesis
The eigenstate thermalization hypothesis, or ETH, says roughly that individual energy eigenstates in a chaotic many-body system already encode thermal expectation values for ordinary local observables.
If a generic initial state is a superposition of many such eigenstates, dephasing among their energies causes observables to settle near thermal values.
ETH is not a universal theorem for every Hamiltonian, but it is a powerful organizing principle for generic non-integrable systems.
Part 3 — Rydberg Atoms Produced the Surprise
Experiments with chains of Rydberg atoms imposed a strong blockade: two neighbouring atoms could not both occupy the Rydberg excited state.
A simplified model, called the PXP model, captures this kinetic constraint.
Most product states in this non-integrable model relax relatively quickly. But a staggered Néel-like configuration such as |1010…⟩ displays repeated oscillations and partial revivals.
the strange behaviour depends strongly on the initial state.
Part 4 — A Sparse Tower of Special Eigenstates
The revival-producing initial state overlaps unusually strongly with a small set of special eigenstates distributed through the many-body spectrum.
These scarred states violate the ordinary ETH expectation: their observable values and entanglement can differ strongly from nearby thermal eigenstates at similar energy density.
They form only a tiny fraction of the exponentially large Hilbert space.
Part 5 — Why Nearly Even Energy Spacing Produces Revivals
Time evolution gives each energy eigenstate a phase factor exp(−iEt/ℏ).
If the important scarred eigenstates have approximately regular energy spacing, their phases can periodically realign.
When that happens, the evolving wavefunction regains large overlap with the initial state and local observables return close to their starting pattern.
The revival is therefore a coherent many-body interference phenomenon, not the system literally running backward in time.
Part 6 — Fidelity Makes the Return Quantitative
A common measure is the return probability or fidelity
F(t) = |⟨ψ(0)|ψ(t)⟩|².
For a generic thermalising initial state, F(t) rapidly becomes very small and irregular.
A scarred initial state can show pronounced recurring peaks. Experiments also track local Rydberg populations, spin observables and entanglement growth.
Part 7 — Why Scars Are Weak Ergodicity Breaking
If nearly every initial state failed to thermalise, we would have strong global non-ergodicity.
Many-body scars are different. Most of the spectrum still looks thermal, and most initial states still relax. The exceptions occupy a thin structured sector.
That coexistence is why scars are so interesting: thermal and nonthermal behaviour live inside the same Hamiltonian.
Part 8 — Scar vs Integrability
An integrable system has many conserved quantities that restrict dynamics for broad families of initial states.
A scarred system can be non-integrable overall. The exceptional dynamics arise from special embedded structures, approximate algebras, constrained trajectories or other mechanisms affecting only selected states.
So observing revivals does not by itself prove the Hamiltonian is integrable.
Part 9 — Scar vs Many-Body Localization
Many-body localization usually relies on strong disorder and produces widespread failure of thermalisation across many eigenstates.
Quantum many-body scars can appear in clean translationally structured systems without quenched disorder and affect only a sparse set of states.
The two mechanisms can both preserve memory, but their spectral and dynamical fingerprints differ.
Part 10 — Low Entanglement Is a Clue, Not a Complete Definition
Many familiar scarred eigenstates have unusually low entanglement compared with nearby thermal states.
This helps explain why simple product states can overlap strongly with them.
But modern work has broadened the landscape. Some scar-like constructions involve different entanglement structures, so “low entanglement” should not be treated as the sole universal definition.
Part 11 — Approximate Algebra Can Organize the Scar Tower
In the PXP model, the special states can be understood partly through an approximate SU(2)-like structure connecting the important scarred eigenstates.
This algebra is not exact in the basic model, which is why revivals decay rather than repeat perfectly forever.
Deforming the Hamiltonian to make this structure more exact can dramatically sharpen revivals—a discriminating test of the mechanism.
Part 12 — 2025: Scar Physics Expanded Beyond the Original PXP Chain
Research in 2025 demonstrated scarred dynamics beyond the original PXP construction, including Rydberg simulators with broader constraints and spinor-gas experiments where selected states remained nonthermal while the majority thermalised.
Physical Review Letters (2025) — Quantum Many-Body Scars Beyond the PXP Model →
Part 13 — 2026: Scarring in Gauge Theories
Current 2026 work is testing how robust scarring remains in more complicated lattice gauge theories with dynamical matter and higher-dimensional structure.
Persistent oscillations, slower entanglement growth and fidelity revivals have been reported in models beyond the simplest one-dimensional spin chains.
This does not mean every revival in every gauge theory is a scar. It expands the set of systems in which the weak-ergodicity-breaking hypothesis can be tested.
Failed Model → Better Model
| Naive model | Why it fails | Better model |
|---|---|---|
| Every non-integrable many-body system forgets every initial state equally. | Sparse nonthermal eigenstates can strongly affect selected initial states. | Resolve the spectrum and initial-state overlaps. |
| Revivals mean the whole system is integrable. | Most states can remain thermal. | Distinguish weak from global ergodicity breaking. |
| Memory means many-body localization. | Scars can occur without disorder. | Check disorder dependence and spectral structure. |
| One oscillating observable proves a scar. | Prethermal, integrable or driven oscillations can mimic revivals. | Combine fidelity, eigenstate, entanglement and perturbation evidence. |
How Do We Know?
- Prepare several different initial product states under the same Hamiltonian.
- Measure local observables versus time.
- Measure or reconstruct return fidelity where possible.
- Compare generic and special initial states.
- Numerically resolve eigenstate expectation values and identify ETH outliers.
- Measure entanglement growth.
- Perturb the Hamiltonian and see whether the scar tower and revivals weaken or sharpen as predicted.
- Compare against integrable and disordered controls.
- Test system-size scaling so finite-size recurrence is not mistaken for a robust scar.
Observation vs Inference
- Observation: certain initial states show repeated many-body revivals.
- Measurement: most other states under the same Hamiltonian relax much more strongly.
- Spectral evidence: atypical nonthermal eigenstates appear embedded in a thermal spectrum.
- Inference: special state-space structure produces weak ergodicity breaking.
- Boundary: revivals alone do not uniquely identify scarring without ruling out integrability, finite-size recurrences, prethermalisation and other mechanisms.
Checkpoint Questions
- What does thermalisation mean for local observables?
- What does ETH predict?
- Why is the Néel-like Rydberg state special?
- How can a tower of eigenstates create revivals?
- Why are scars called weak ergodicity breaking?
- How do scars differ from integrability?
- How do they differ from many-body localization?
- Why is low entanglement only a clue?
- What evidence is stronger than one oscillating observable?
- Why must finite-size effects be checked?
Answer Key
Open after attempting the questions
- They approach values largely independent of microscopic details of the initial state.
- Typical many-body eigenstates give thermal local expectation values.
- It overlaps strongly with a sparse scarred subspace.
- Nearly regular energy spacings let phases periodically realign.
- Most of the Hilbert space remains thermal.
- Integrability constrains broad dynamics through many conserved quantities.
- Many-body localization generally involves disorder and widespread nonthermal states.
- Not all modern scar-like mechanisms share one entanglement pattern.
- Fidelity revivals, ETH-outlier eigenstates, entanglement structure and controlled perturbations together.
- Small isolated systems naturally recur eventually even without robust scar physics.
Primary Science Bridge
- systems can remember or forget starting patterns;
- some starting patterns are more special than others;
- waves can re-align and create revivals;
- a few exceptions do not mean every case follows the exception;
- repeated measurements help distinguish a real pattern from coincidence.
Secondary and JC Bridge
| Core idea | Higher-resolution route |
|---|---|
| Thermalisation | Eigenstate thermalization hypothesis |
| Superposition | Many-body phase evolution |
| Recurrence | Fidelity revival |
| Entanglement | Thermal versus scarred eigenstates |
| Ergodicity | Weak ergodicity breaking |
| Quantum simulation | Rydberg constraints and gauge theories |
Unfamiliar Transfer Challenge
A quantum simulator shows long-lived oscillations from one initial state but not from dozens of others.
What would make a many-body-scar interpretation stronger? Resolve nonthermal eigenstates embedded in the thermal spectrum, measure revival fidelity and entanglement, test system-size scaling, and perturb the Hamiltonian in ways predicted to destroy or enhance the scar subspace.
Deep Science Window — Hilbert-Space Geometry
A many-body wavefunction evolves through an enormous Hilbert space. Scarred dynamics can be understood as motion that remains unusually concentrated near a special low-dimensional manifold rather than exploring the available space democratically. This geometric picture helps connect many-body scars with semiclassical periodic orbits without claiming the two problems are identical.
Deep Science Window — Perfect vs Approximate Scars
Some engineered Hamiltonians contain exact scar eigenstates protected by algebraic structure. The original PXP scars are approximate: their energy spacing is not perfectly uniform and the revivals decay. Distinguishing exact from approximate constructions prevents one label from hiding important dynamical differences.
Evidence Boundaries
- Quantum scar ≠ every long-lived oscillation.
- Weak ergodicity breaking ≠ whole system fails to thermalise.
- Scar ≠ integrability.
- Scar ≠ many-body localization.
- Low entanglement ≠ universal standalone definition.
- Finite-size revival ≠ robust thermodynamic scar without scaling evidence.
Manual Summary — KNOW → CONNECT → EXPLAIN → APPLY → CHECK
KNOW: ETH, thermalisation, scarred eigenstate, revival, fidelity, weak ergodicity breaking.
CONNECT: special eigenstate tower to strong initial-state overlap, phase re-alignment and coherent revivals.
EXPLAIN: why one initial state can retain memory in a Hamiltonian that thermalises most others.
APPLY: distinguish a candidate scar from integrable, localized or finite-size dynamics.
CHECK: require spectral and dynamical evidence, not merely a striking oscillation plot.
Teaching Guide for Parents, Tutors and Teachers
Begin with memory loss in an interacting system, then introduce one exceptional initial state. Avoid presenting scars as “quantum systems never thermalise.” The exception is educationally useful precisely because the surrounding spectrum mostly does thermalise.
- Define thermalisation operationally.
- Introduce ETH.
- Compare generic and special initial states.
- Build the eigenstate-tower picture.
- Connect regular energy spacing to revival.
- Contrast integrability and localization.
- Add entanglement and system-size evidence.
- Finish with 2025–2026 extensions and naming boundaries.
Independent check: later show an oscillating finite quantum system and ask students for at least three non-scar explanations that must be excluded.
Safety boundary: experimental many-body-scar platforms use lasers, ultracold atoms, vacuum systems and precision control. Use published datasets and simulations for ordinary teaching.