Takeaway

In disordered interacting systems, eigenstates can fail to thermalize; local memory persists indefinitely, violating the eigenstate thermalization hypothesis.

The problem (before → after)

  • Before: Generic interacting systems act as their own heat baths; observables relax to thermal values.
  • After: Strong disorder and interactions produce emergent local integrals of motion (LIOMs) that preserve information and block transport.

Mental model first

Picture traffic on a highway jammed by random lane closures: cars (excitations) can’t pass, so local patterns persist rather than mixing into a uniform flow.

Just-in-time concepts

  • ETH vs MBL: Thermal eigenstates mimic Gibbs ensembles; MBL eigenstates area-law entangled and retain initial conditions.
  • LIOMs (ℓ-bits): Quasi-local conserved quantities diagonalizing the Hamiltonian.
  • Signatures: Poisson level statistics, logarithmic entanglement growth, vanishing DC conductivity.

First-pass solution

Introduce quenched disorder to an interacting chain (e.g., XXZ + random fields). Simulate quenches; observe failure to thermalize and logarithmic entanglement growth.

Iterative refinement

  1. Stability: MBL vs rare-region (Griffiths) effects; avalanches can destabilize in higher dimensions.
  2. Experiments: Cold atoms and trapped ions show signatures via imbalance decay.
  3. Mobility edge: Transition energy separating localized and delocalized states.

Principles, not prescriptions

  • Disorder can protect quantum information by hindering transport.
  • Entanglement structure diagnoses phases of dynamics.

Common pitfalls

  • Confusing Anderson localization (noninteracting) with MBL; interactions change scaling and dynamics.
  • Finite-size numerics can mislead; use multiple diagnostics.

Connections and contrasts

  • See also: [/blog/decoherence], [/blog/quantum-error-correction], [/blog/graph-neural-networks] (learning LIOM structure is an open ML task).

Quick checks

  1. What breaks ETH in MBL? — Emergent local integrals of motion.
  2. Why logarithmic entanglement growth? — Dephasing via exponentially decaying interactions among ℓ-bits.
  3. How to distinguish from Anderson localization? — Interaction-dependent signatures and dynamics.

Further reading

  • Abanin, Altman, Bloch, Serbyn reviews
  • Source preprint (above)