Does the random SU(2) Heisenberg magnet freeze at zero temperature? · revision history
Revision 1
Accepted · first revision · record
- Title
- Does the random SU(2) Heisenberg magnet freeze at zero temperature?
- Plain
- When quantum spins free to point in any direction interact with random couplings of both signs, they may freeze into a glass or stay in a liquid-like state with no frozen moments. For spin $1/2$ with all-to-all random couplings, calculations suggest weak freezing, but its size and the liquid-like behavior above it are unsettled, and short-range versions are open.
- Precise
- Model: $H = (1/\sqrt{N}) \sum_{i<j} J_{ij} S_i . S_j$, $S = 1/2$, $J_{ij}$ independent Gaussian with zero mean and unit variance, and its short-range versions on 2D and 3D lattices. Determine whether the Edwards-Anderson order parameter $q_{\mathrm{EA}}$, the long-time limit of the site- and disorder-averaged $\langle S_i(t) . S_i(0)\rangle$, is nonzero at $T = 0$ in the thermodynamic limit, its value, and the temperature window in which Sachdev-Ye spin-liquid correlations $G(\tau)\sim 1/\tau$ appear. An answer gives $q_{\mathrm{EA}}$ with error bars and the crossover temperature.
- Settled by
- Extrapolation in N of exact-diagonalization and matrix-product-state data for the infinite-range model, checked against controlled large-M expansions of its SU(M) generalization, and quantum Monte Carlo or tensor-network data for the lattice versions.
- Kind
- well-posed
- Answer type
- value
- References
- (empty)
- Literature status
- partially-resolved
- Status note
- Christos, Haehl and Sachdev (PRB 2022) described spin-glass order at $T = 0$ with a spin-liquid crossover at higher $T$, and Hosseinabadi, Sachdev and Marino (PRL 2026) studied the crossover to Sachdev-Ye-Kitaev criticality; the short-range lattice versions are open.
- Posed since
- 1993