QM Seminar Speaker Paul Fendley (Oxford) Wednesday, April 24

Time: 2:00 pm, Wednesday, April 24
Venue: Old LeConte 402
Title: Supersymmetry and free fermions from interacting Majorana fermions 
Abstract: Perturbing a quantum spin/Majorana chain with a self-dual four-fermi terms leads to tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. I explain how supersymmetry is not only an emergent property of the scaling limit, but give an example where explicit lattice expressions for the supersymmetry generators and currents can be found. Writing the Hamiltonian in terms of these generators allows us to find the ground states exactly at a frustration-free coupling. At the strongly interacting pure four-fermi point, the model can be solved using free-fermion raising and lowering operators, giving a gapless system with dynamical critical exponent z=3/2. I will also explain how a parafermionic generalization yields interesting multicritical points along with an AKLT phase. At the AKLT point, a map to the ordered dual model makes it straightforward to find some exact excited states as well as the ground state.

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