BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Adrian Chapman (University of Sydney) DTSTART:20200707T010000Z DTEND:20200707T020000Z DTSTAMP:20260423T041812Z UID:UTSQSI/14 DESCRIPTION:Title: Characterization of free-fermion-solvable spin models via graph invariants \nby Adrian Chapman (University of Sydney) as part of Centre for Quant um Software and Information Seminar Series\n\n\nAbstract\nFinding exact so lutions to spin models is a fundamental problem of many-body physics. A wo rkhorse technique for exact solution methods is mapping to an effective de scription by noninteracting fermions. The paradigmatic example of this is the Jordan-Wigner transformation for finding an exact solution to the one- dimensional XY model. Another important example is the exact free-fermion solution to the two-dimensional Kitaev honeycomb model. \n\nI will describ e a framework for recognizing general models which can be solved this way by utilizing the tools of graph theory. Our construction relies on a conne ction to the graph-theoretic problem of recognizing line graphs\, which ha s been solved optimally. A corollary of this result is a complete set of c onstant-sized frustration structures which obstruct a free-fermion solutio n. We classify the kinds of Pauli symmetries which can be present in model s for which a free-fermion solution exists\, and we find that they corresp ond to either: (i) gauge qubits\, (ii) cycles on the free-fermion hopping graph\, or (iii) the fermion parity. Clifford symmetries\, except in finit ely-many cases\, must be symmetries of the free-fermion Hamiltonian itself . We expect our characterization to motivate a renewed exploration of free -fermion-solvable models\, and I will close with an elaborate discussion o f how we expect to generalize our framework beyond generator-to-generator mappings.\n LOCATION:https://researchseminars.org/talk/UTSQSI/14/ END:VEVENT END:VCALENDAR