Analysis/Mathematical Physics Seminar

The spin-S quantum spin chain, with a projection-based antiferromagnetic interaction, and the antiferromagnetic XXZ spin-1/2 chain exhibit different forms of translation symmetry breaking. Yet they are related to a common system of random loops, which is similar to the collection of the boundaries of a classical, two dimensional, Q-state random cluster model. We use these relations to establish the exact conditions for symmetry breaking, in a manner similar to the recent proofs of the discontinuity of the phase transition for Q > 4. The quantum transitions in each case is from a gapless ground state to a pair of gapped and extensively distinct ground states. Joint work with H. Duminil-Copin and S. Warzel).