Exponentially small gaps inside the quantum spin-glass phase
In plain words
Below the critical sideways field, the two lowest energy levels of a spin glass can approach each other and swap order as the field is reduced, and each near-crossing forces a quantum annealer to slow down. Whether such near-crossings occur in typical large samples, and how small their gaps become, decides whether annealing is exponentially slow even after the critical point is passed.
Precise statement
For the transverse-field Edwards-Anderson model in $d = 2\ \text{and}\ 3$, and its infinite-range (Sherrington-Kirkpatrick) limit, at $0 < \Gamma < \Gamma_c$, determine the probability that the instantaneous ground state has an avoided crossing as $\Gamma$ decreases to 0, and the scaling of the minimum gap $\Delta_{\min}$ with N: $\exp(-c N^a)$ with the value of a, or a power law. An answer gives the typical $\Delta_{\min}(N)$ and its distribution over disorder samples.
What would settle it
Exact diagonalization and parity-resolved quantum Monte Carlo or tensor-network tracking of the two lowest levels along $\Gamma$ for $N$ up to a few hundred spins over many disorder samples.
Status in the literature
Knysh (Nature Communications 2016) argued that such bottlenecks are generic in the spin-glass phase and give gaps exponentially small in N; tests in finite dimensions remain limited.
Results
No results have been posted on this problem yet.
Post a result · how results are checked
Sign in to follow or save this problem
See also
- Related Replica symmetry breaking or droplets in the 3D Edwards-Anderson model
- Related Does quantum annealing outscale classical algorithms on 3D spin glasses?
- Related Asymptotic scaling of coherent quantum annealing in 3D spin glasses
- Related How the energy gap closes at the 3D quantum spin-glass transition
Comments (0)
Comments are not records: they are not signed, stamped or logged. How comments work
No comments yet.
Sign in to comment.