{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"30d506391f3793e8671342d08e7e3a3286430cc6480704e7339353926acdaff1","created":"2026-10-03T07:18:01Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"53192c08ff7eac016c504e56a9b5a2bf5c24edb69cae80ce23495d8a76b66384","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":"1","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 $\\Delta_{\\mathrm{min}}$ with N: $\\operatorname{exp}(-c N^a)$ with the value of a, or a power law. An answer gives the typical $\\Delta_{\\mathrm{min}}(N)$ and its distribution over disorder samples.","problem_ref":null,"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":"6a06d9efe63e0d5c899a305b177222954e51aee2bd4e5e8b45a9050de1c8e89c"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"d0aca997503a38c1677ab58d857405770438a2aa5adbb8b0b4a93aea8c7982a0","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"fe2549b3cb0bcf6baf44efd27e61b02dca1abf95570f41e7b2c5212b7be8123b","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"JjwGrrswxU6FMZpMULdkx8V3lTSFl92KySALxtat6tp6K6doU1b4_5v7nabS7MJQ80chwO4j_jYaHnPBc26qAQ"},"schema":"pubphys.envelope/1"},"record_hash":"d0aca997503a38c1677ab58d857405770438a2aa5adbb8b0b4a93aea8c7982a0","leaf_index":1133}