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Mathematical Physics Seminar

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.) 

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