Is the random-field Heisenberg chain localized at strong disorder? · revision history

Revision 2

Accepted · core change · record

Changes against revision 1:

Title · changed
Revision 1: Is the random-field Heisenberg chain localized at strong disorder
Revision 2: Is the random-field Heisenberg chain localized at strong disorder?
Plain
The standard test case is a chain of quantum spins in random magnetic fields of strength W. The question is whether, for large enough W, an infinitely long chain stays out of equilibrium forever.
Precise · changed · core
Revision 1: $H = \sum_i J S_i . S_{i+1} + h_i S^{z}_i$ with h_i independent and uniform in $[-W, W]$. Does a $W_c < \infty$ exist such that for $W > W_c$ infinite-temperature eigenstates obey an area law and local memory of the initial state persists as $t \to \infty$, in the limit $L \to \infty$? Answer yes or no, with an estimate or bound on $W_c$.
Revision 2: $H = \sum_i J S_i . S_{i+1} + h_i S^{z}_i$ with $h_i$ independent and uniform in $[-W, W]$. Does a $W_c < \infty$ exist such that for $W > W_c$ infinite-temperature eigenstates obey an area law and local memory of the initial state persists as $t \to \infty$, in the limit $L \to \infty$? Answer yes or no, with an estimate or bound on $W_c$.
Settled by
A proof for this model (Imbrie's 2016 proof covers a random Ising chain with transverse field and relies on an unproven limited-level-attraction assumption), or numerics that control rare thermal regions at sizes where avalanche effects are visible.
Kind
well-posed
Answer type
yes-no
References
(empty)
Literature status
contested
Status note
Avalanche studies (Morningstar et al. 2022, arXiv:2107.05642) place any transition at disorder well above the exact-diagonalization crossover W of about 4J; existence itself remains debated in 2025-2026.
Posed since
2006

Decisions