Seminars & Colloquia Calendar
Geometric analysis of frustration in a class of SU(2S+1) invariant quantum spin chains
Michael Aizenman - Princeton University
Location: Hill 705
Date & time: Thursday, 17 October 2019 at 12:00PM - 1:00PM
Abstract: Unlike their classical counterparts, quantum antiferromagnetic systems exhibit ground state frustration effects even in one dimension. A case in point is the SU(2S+1) invariant spin chain, with the interaction between pairs of neighboring S-spins given by a one dimensional projection on the pair’s total spin zero state.
We show that in the infinite volume limit for any S>1/2 the system has a pair of distinct ground states, each gapped and exhibiting spatial energy oscillations. The analysis utilizes a stochastic geometric representation of the system’s thermal states, which allows to apply to this quantum system methods which were originally developed in the context of the classical Q-state Potts model.
(Talk based on a joint work with Hugo Dumnil-Copin.)