{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"ae53fcd58923988ef811e0e033fc343cbfbfe882c318a18dfa8bad7e81a65b7f","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","d0aca997503a38c1677ab58d857405770438a2aa5adbb8b0b4a93aea8c7982a0"],"salt":"2d4bb1a47fa5580f071bb0e4a770517ceb26297d902f174a2a8bcccb642ff95c","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"cm.quantum-spin-glasses.glass-phase-bottlenecks","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"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.","posed_since":"","precise":"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.","problem_ref":"d0aca997503a38c1677ab58d857405770438a2aa5adbb8b0b4a93aea8c7982a0","references":"","settled_by":"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_note":"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.","title":"Exponentially small gaps inside the quantum spin-glass phase","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"ef31b45595a19f481e14edb681899a496da7e9ebb54fc0cbd022c6642e2de433","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"cdeb23b87f7b96ab944cdd1778f3cd29fbb8054ec2cabf490103a1b53f830159","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"GbTN9G50GqkG-qB2lWloTALMI5lPqmLU-gFtinQmhXhCgyaOyMap-s--M3CT_MRo8RESdydHAu7XecFYjjOzBg"},"schema":"pubphys.envelope/1"},"record_hash":"ef31b45595a19f481e14edb681899a496da7e9ebb54fc0cbd022c6642e2de433","leaf_index":2998}