BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Anton Kapustin (Caltech) DTSTART:20211213T170000Z DTEND:20211213T180000Z DTSTAMP:20260423T005807Z UID:QM3/60 DESCRIPTION:Title: Hig her Berry classes for many-body quantum lattice systems\nby Anton Kapu stin (Caltech) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nA bstract\nM. Berry showed how to attach a line bundle and a connection on i t to a family of quantum Hamiltonians with a non-degenerate ground state\, under the assumption that the Hilbert space is finite-dimensional. The fi rst Chern class of this line bundle is a topological invariant of the fami ly. It is far from obvious if this construction can be generalized to qua ntum many-body Hamiltonians. Indeed\, naive generalizations fail because g round states of different Hamiltonians typically correspond to inequivalen t representations of the algebra of observables. Nevertheless\, it is poss ible to construct such invariants by making use of a certain differential graded Lie algebra (DGLA) attached to a quantum lattice system. For exampl e\, it turns out that to any family of gapped Hamiltonians on a 1d lattice one can attach a “quantized” degree-3 cohomology class on the paramet er space. In this talk I will outline a construction of this DGLA as well as the construction of higher Berry classes. The talk is based on a work i n progress with Nikita Sopenko.\n LOCATION:https://researchseminars.org/talk/QM3/60/ END:VEVENT END:VCALENDAR